Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea

EAIIIA TH??e A?eai?iae/

OAeE
512.54

I?IAEAIA NI?ssAEAIINO? OA ??NO IA??IAe?A O A?OIAO A?EAI?*OEA.

(01.01.06 – aeaaa?a oa oai??y /enae)

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Ee?a 1999

Aeena?oaoe??th ? ?oeiien.

?iaioo aeeiiaii a Ee?anueeiio oi?aa?neoao? ?i. Oa?ana Oaa/aiea.

Iaoeiaee ea??aiee:

NOUAINEEE A?oae?e ?aaiiae/, aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?,
caa?aeoth/ee eaoaae?e aeaaa?e ? iaoaiaoe/ii? eia?ee Ee?anueeiai
oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea, i. Ee?a

Io?oe?ei? iiiiaioe:

A?EAI?*OE ?inoeneaa ?aaiiae/, aeieoi? o?ceei-iaoaiaoe/ieo iaoe,
i?ioani?, i?ia?aeiee iaoeiaee ni?a?ia?oiee iaoaiaoe/iiai ?inoeoooo ?i.
A. A. No?eeiaa ?AI, i. Iineaa

Aiaeia?/oe TH??e A?eoi?iae/, eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe,
aeioeaio oi?aa?neoaoo «Ee?ai-Iiaeeyinueea aeaaeai?y», i. Ee?a

I?ia?aeia onoaiiaa:

Euea?anueeee aea?aeaaiee oi?aa?neoao ?i. ?. O?aiea

Caoeno a?aeaoaeaoueny ” 15 ” _ethoiai_ 1999 ?ieo i 14 aiae. ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.001.18 i?e Ee?anueeiio
oi?aa?neoao? ?i. Oa?ana Oaa/aiea ca aae?anith: 252127, i. Ee?a, i?.
aeaae. Aeooeiaa, 6, iaoai?ei-iaoaiaoe/iee oaeoeueoao.

C aeena?oaoe??th iiaeia iciaeiieoeny a a?ae?ioaoe? Ee?anueeiai
oi?aa?neoaoo ?i. Oa?ana Oaa/aiea (aoe. Aieiaeeie?nueea, 58).

Aaoi?aoa?ao ?ic?neaii ” _11_ ” __n?/iy_ 1999 ?ieo.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee
IAO?AA*OE A. I.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. O 1902 ?ioe? O. Aa?inaeae noi?ioethaaa ?yae
i?iaeai, ye? aeiaaee /an noeioethaaee i noeioeththoue aaaaoi/enaeuei?
aeine?aeaeaiiy a oai??? a?oi.

Caaaeueia i?iaeaia Aa?inaeaea: ”*e aoaea aeia?eueia ia??iaee/ia
a?oia eieaeueii ne?i/aiiith?” io?eiaea iaaaoeaia ?ica’ycaiiy a ?iaio? A.
N. Aieiaea1 eeoa a 1964 ?ioe?. A 1972 ?ioe? N. A. Aeueioei2 iiaoaeoaaa
ia??iaee/io a?oio, yea ii?iaeaeo?oueny aeaiia aaoiiaoieie ia?aoai?aiiyie
? ? iane?i/aiiith. Eiaeai c aaoiiaoia caaaea? iiaenoaiiaeo ia neiaao
iaae aeoaaioii, ui neeaaea?oueny ?c aeaio neiaie?a.

Aeei?enoiaoth/e iiao aaoiiaoieo ia?aoai?aiue ca aeiiiiiaith
?icaeiooi? E. A. Eaeoaei?iei oai??? iane?i/aiieo a?ioeaaeo aeiaooe?a
?-a?oi3,

A. ?. Nouainueeee a 1979 ?ioe? caoaeoaaa i?eeeaae iane?i/aiii? p-a?oie,
ii?iaeaeaii? aeaiia aeaiaioaie ii?yaeeo p, p?2. 4

)5 .

Eiino?oeoe?y ia??iaee/ii? ia eieaeueii ne?i/aiii? a?oie aeicaieeea

?. ? . A?eai?/oeia? a 1984 ?ioe? aeaoe a?aeiia?aeue ia oe?eee ?yae ?ioeo
oe?eaaeo ieoaiue6.

1 Aieiae A. N. I ieeue-aeaaa?ao e oeieoii aii?ieneie?oaiuo
a?oiiao // Eca. AI NNN?. Na?. Iaoai. 1964. O. 28. ?2. N.
273–276.

2 Ae?oei N. A. Eiia/iua aaoiiaou e i?iaeaia Aa?inaeaea i
ia?eiaee/aneeo a?oiiao //

Iao. caiaoee. 1972. O. 11. ?3. N.319–328.

3 Eaeoaeiei E. A. La structure des p-groupes de sylow des groupes
symetriques finis // Ann. Ec. Normale. 1948. V. 3(65). P. 239–276.

4 Nouaineee A. E. Ia?eiaee/aneea iiaea?oiiu iiaenoaiiaie e
iaia?aie/aiiay i?iaeaia Aa?inaeaea //AeAI NNN?. 1979. O. 247. ?3.
N. 561–565.

5 A?eai?/oe ?. E. E i?iaeaia Aa?inaeaea i ia?eiaee/aneeo a?oiiao
// Ooieoe. aiaeec e aai i?eeiae. 1980. O. 14. Aui. 1. N. 53–54.

6 A?eai?/oe ?. E. Noaiaie ?inoa eiia/ii-ii?iaeaeaiiuo a?oii e oai?ey
eiaa?eaioiuo n?aaeieo // Eca. AI NNN?. Na?. Iaoai. 1984. ?5. N. 939–985.

A naia: iiai?oa aea/aiiy oei?? a?oie oa ?ioeo 2-a?oi noiaei?
eiino?oeoe?? i?eaaei aei ?ica’ycaiiy i?iaeaie I?eii?a7 i?i a?oiiaee
??no.

.

Ooieoe?y ?inoo eiaeii? 2-a?oie A?eai?/oea

? oaeaeoa aoaeue-yei? noaiaiaai? ooieoe?? (?c oi/i?noth aei
aea?aaeaioiino?):

.

Caoaaaeeii, ui a?oie A?eai?/oea G( a eiai caaaeuei?e eiino?oeoe?? 6
aoaeothoueny ia iniia? iane?i/aiieo iine?aeiaiinoae ( iaae aeoaa?oii
{1,2,3}.

A ?iaio? 8 I. Aeae iinoaaea ieoaiiy i?i ca?aei?noue eean?a
aiaiaaaeueieo a?oi ? o. ca. aeaiaioa?ieo a?oi, ui ooai?ththoueny ?c
ne?i/aieo ? aaaeaaeo a?oi ??ciiiaieoi?oieie canoinoaaiiyie /ioe?ueio
iia?aoe?e: acyooy i?aea?oie, acyooy oaeoi?-a?oie, a?oiiaiai ?icoe?aiiy,
oa ?iaeoeoeaii? a?aieoe?. I?eeeaae a?oi A?eai?/oea5 aeaa iaaaoeaio
a?aeiia?aeue ia ieoaiiy Aeay, oiio ui ?c iaeiiai aieo iane?i/aiia
ne?i/aiii ii?iaeaeaia ia??iaee/ia a?oia ia iiaea aooe aeaiaioa?iith9, a
c ae?oaiai – a?oia ia aeniiiaioe?eiiai ?inoo aiaiaaaeueia10.

Ia??iaee/i? a?oie A?eai?/oea c ?iaioe6 iathoue o?ea?aeueiee oeaio?,
eiaeia aeania ?o oaeoi?-a?oia ? ne?i/aiiith ? aiie caaeiaieueiythoue
oiia? iaeneiaeueiino? aeey noaii?iaeueieo i?aea?oi, ui aeaei ciiao ?.?.
A?eai?/oeo aeaoe iiceoeaio a?aeiia?aeue ia a?aeiia ieoaiiy I?aeaea6.

7 Milnor J. Problem 5603 // Amer. Math. Monthly. 1968. V. 75. ?6. P.
685–686.

8 Day M. Amenable semigroups // III. J. Math. 1957. V. 1. P. 509–544.

9 Chou C. Elementary amenable groups // III. J. Math. 1980. V. 24.
?3. P. 396–406.

10 Aaeaeueaenii-Aaeueneee A. I., O?aeaea? TH. A. Aaiaoiai n?aaeiaa ia
a?oiiao // Oniaoe iaoai. iaoe. 1957. O. 12. Aui. 6. N. 131–136.

Eiino?oeoe?y a?oi G( oaeiae aeei?enoiao?oueny aeey ciaoiaeaeaiiy
?ioeo i?eeeaae?a oe?eaaeo a?oi. Aeei?enoiaoth/e ocaaaeueiaiiy a?oi G( ia
aeiaaeie

p-a?oi ?. ?. A?eai?/oe ciaeoia p-a?oie i?ii?aeiiai c?inoo, c
eiioeioaeueiei /eneii oaeoi?-a?oi11; aeei?enoiaoth/e eiino?oeoe?th a?oi
c ?iaioe6 iei oaeiae io?eiaii i?eeeaae ne?i/aiii aecia/aii?
aiaiaaaeueii? ia aeaiaioa?ii? a?oie18.

A i?iiiiiaai?e aeena?oaoe?ei?e ?iaio? aaoi? i?iaeiaaeo? aea/aiiy
2-a?oi A?eai?/oea. ?ioa?an aei iiae?aieo eiino?oeoe?e c?inoa?, oiio
oe?eeii i?e?iaeii aeey 2-a?oi A?eai?/oea noi?ioethaaoe iniiai? i?iaeaie
eiia?iaoi?ii? oai??? a?oi. I?iaeaia ??aiino? ne?a aeey aoaeue-yei?
ia??iaee/ii? a?oie A?eai?/oea G( ?ica’yco?oueny ”i?e?iaeiei” /eiii6:

A naia, G( ia? ?ica’ycio i?iaeaia ??aiino?, oiae? e eeoa oiae? eiee
oa??i? aeaiaioe oe??? a?oie iiaeooue aooe aecia/ai? ?aeo?neaii. ?ioeie
neiaaie, yeui G( caoaeiaaia ca ?aeo?neaiith iine?aeiai?noth (, oi a G(
iiceoeaii ?ica’yco?oueny i?iaeaia ??aiino? ? iaaiaee.

I?ioa, i?iaeaia ni?yaeaiino? aeaiaio?a aeey a?oi G( aeiaaee /an
caeeoaeanue a?aee?eoith. A ?icae?e? 2 oe??? ?iaioe aaoi? io?eio?
e?eoa??e ni?yaeaiino? aeaiaio?a a 2-a?oiao A?eai?/oea ? iiai?noth
?ica’yco? oeth i?iaeaio.

Iaei??th c eiiaeiaoi?ieo oa?aeoa?enoee ia??iaee/ii? iane?i/aiii?
ne?i/aiii ii?iaeaeaii? a?oie G ? ?? ooieoe?y ?inoo ia??iae?a, yea
aecia/a?oueny oaeei /eiii:

11 A?eai?/oe ?. E. Eiino?oeoeey ?–a?oii i?iiaaeooi/iiai ?inoa,
iaeaaeathuay eiioeieooiii oaeoi?-a?oii // Aeaaa?a e eiaeea. 1984. 24.
?4. N. 383–394.

12 A?eai?/oe ?. E. I?eia? eiia/ii ii?aaeaeaiiie aiaiaaaeueiie a?oiiu,
ia i?eiaaeeaaeauae eeanno EG // Iaoai. na. 1998. ?1. O. 189. N. 79–100.

I/aaeaeii, ui iiaaae?iea ooieoe?? ?inoo ia??iae?a iaaiei /eiii aieeaa?
ia caaaeuei? aeanoeaino? a?oie. Caaaea?ii, iai?eeeaae, a?aeiio oai?aio
Caeueiaiiaa13 i?i ne?i/aii?noue ?aceaeoaeueii ne?i/aiieo a?oi, a yeeo
ooieoe?y ?inoo ia??iae?a iaiaaeaia. A aeai?e ?iaio? ie i?iaeiaaeo?ii
oaeiae aeine?aeaeaiiy ooieoe?? ?inoo ia??iae?a a a?oiao A?eai?/oea G(
yea ?icii/aeinue ua a 6 .

Iaoa ?iaioe. Iaoith i?iiiiiaaii? aeena?oaoe?eii? ?iaioe ? i?iaeiaaeaiiy
aea/aiiy 2-a?oi A?eai?/oea oa aeayeeo ?ioeo a?oi noiaei? eiino?oeoe??.

Iiai?noueth ?ic’ycaii i?iaeaio ni?yaeaiino? aeaiaio?a a 2-a?oiao
A?eai?/oea. Io?eiaii iia? ioe?iee cieco oa caa?oo aeey ooieoe?e ?inoo
ia??iae?a oeeo a?oi. Aeey a?eueo oe?ieiai eeano o.ca. ?icaaeoaeoaaeueieo
a?oi ( a yeee aoiaeyoue ? 2-a?oie A?eai?/oea ) anoaiiaeth?oueny
a?aenooi?noue oioiaeiinoae, a eiaei?e c a?oi oeueiai eeano.

?icaeiooi niaoe?aeueiee oaoi?/iee aia?ao aeey aea/aiiy a?oi
A?eai?/oea G(, ui aaco?oueny ye ia iia? ”ia?aeeaaeaiue” i?ae?ioa?aae?a
?ioa?aaeo (0,1), oae ? ia iiaao oai??? a?oi aaoiii?o?ci?a ei?aiaaeo
aea?aa ? iane?i/aiieo a?ioeaaeo aeiaooe?a a?oi.

Iaoiaee aeine?aeaeaiiy. A aeena?oaoe?ei?e ?iaio? aeey aea/aiiy a?oi
A?eai?/oea canoiniaothoueny iaoiaee eiia?iaoi?ii? oai??? a?oi ? oai???
a?oi i?aenoaiiaie. Cie?aia, aeei?enoiao?oueny oai??y a?oiiaeo ae?e ia
aea?aaao.

Iaoeiaa iiaecia. A aeena?oaoe?ei?e ?iaio? aaoi?ii io?eiai? oae? iia?
?acoeueoaoe:

iieacaii, ui i?iaeaia ni?yaeaiiino? aeey 2-a?oi A?eai?/oea
?ica’yco?oueny iiceoeaii oiae? e eeoa oiae? eiee iiceoeaii
?ica’yco?oueny i?iaeaia ??aiino?;

aeey oe?ieiai i?aeeeano a?oi A?eai?/oea io?eiaii ioe?iee cieco aeey
ooieoe?e ?inoo ia??iae?a oeeo a?oi;

13 Zelmanov E. I. The solution of the restricted Burnside problem for
groups of prime power order // Yale Universty Notes. 1990.

aeey an?o 2-a?oi A?eai?/oea aeaco?oueny iiaa ioe?iea caa?oo aeey ?o
ooieoe?e ?inoo ia??iae?a. Cie?aia, anoaiiaeth?oueny, ui oey ioe?iea oei
oi/i?oa, /ei oi/i?oa ioe?iea caa?oo aeey ooieoe?e ?inoo oeeo a?oi;

anoaiiaeth?oueny, ui a?oie c aaeeeiai i?aeeeano ne?i/aiii ii?iaeaeaieo
?aceaeoaeueii ne?i/aiieo a?oi ia iathoue (iao?ea?aeueieo) oioiaeiinoae.
Cie?aia, aoaeue-yea ?icaaeoaeoaaeueia a?oia ia ia? oioiaeiinoae.

Oai?aoe/ia oa i?aeoe/ia oe?ii?noue aeena?oaoe??. ?acoeueoaoe
aeena?oaoe?? ? iaaiei aeeaaeii a oai??th ?aceaeoaeueii ne?i/aiieo a?oi.
Iaoiae?ea aeine?aeaeaiue iiaea aooe ia?aianaii ia oe?o? eeane
?aceaeoaeueii ne?i/aiieo a?oi, a ?icaeiooa oaoi?ea aeei?enoaia i?e
aea/aii? ?ioeo a?oi aaoiii?o?ci?a eieaeueii ne?i/aiieo aea?aa.

Ai?iaaoe?y ?iaioe. Io?eiai? a aeena?oaoe?? ?acoeueoaoe aeiiia?aeaeenue
ia nai?ia?? ”Oai??y a?oi oa iai?aa?oi” o Ee?anueeiio oi?aa?neoao? ?iai?
Oa?ana Oaa/aiea; ia IV I?aeia?iaei?e eiioa?aioe?? ”A?oie oa a?oiia?
e?eueoey” (i. Aaeeeee Etha?iue,1996 ??e); ia I?aeia?iaei?e eiioa?aioe??,
i?enay/ai?e iai’yo? i?ioani?a E. I. Aeone?ia (i. Neia’yinuee, 1997); ia
V? I?aeia?iaei?e eiioa?aioe?? ”A?oie oa a?oiia? e?eueoey” (i.A?nea,
Iieueoa, 1998 ??e); ia I?aeia?iaei?e iaoaiaoe/i?e eiioa?aioe??,
i?enay/ai?e iai’yo? E. N. Iiio?ya?ia (i. Iineaa, ?in?y, 1998 ??e).

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaai? a 4 iaoeiaeo
noaooyo, a oaeiae o 4 oacao aeiiia?aeae iaoeiaeo eiioa?aioe?e. Nienie
?ia?o iaaaaeaiee iai?ee?ioe? aaoi?aoa?aoo.

Iniaenoee aianie aeena?oaioa. An? ?acoeueoaoe aeena?oaoe?? io?eiaii
aaoi?ii naiino?eii.

No?oeoo?a ? ia’?i ?iaioe. Aeena?oaoe?eia ?iaioa neeaaea?oueny c?
anooio, o?ueio ?icae?e?a ? nieneo e?oa?aoo?e, aeeeaaeaieo ia 117
noi??ieao iaoeiiieniiai oaenoo. Nienie e?oa?aoo?e i?noeoue 42
iaeiaioaaiiy.

CI?NO ?IAIOE

O anooi? aeeeaaeaii iaeyae iniiaii? e?oa?aoo?e ca oaiith
aeena?oaoe??, noi?ioethaaiii iniiai? ?acoeueoaoe aeena?oaoe?eii?
?iaioe.

A ia?oiio ?icae?e? aea?oueny aecia/aiiy a?oi A?eai?/oea,
i?eaiaeyoueny iniiai? a?aeii? aeanoeaino? oeeo a?oi, aecia/a?oueny iiaa,
ca aeiiiiiaith yei? aoaeooue aea/aoenue oe? a?oie. A i?ae?icae?e? 1.2
aeey aea/aiiy a?oi A?eai?/oea a oa?i?iao iane?i/aiieo a?ioeaaeo
aeiaooe?a ?icaeiooi iaaiee oaoi?/iee aia?ao, oa iaaaaeaii e?eueea
aeiiii?aeieo oaa?aeaeaiue.

Iniiaiei ?acoeueoaoii ae?oaiai ?icae?eo ? oaea

OAI?AIA 2.2.5. I?iaeaia ni?yaeaiino? a a?oi? A?eai?/oea G(
?ica’yco?oueny iiceoeaii oiae? ? eeoa oiae?, eiee a i?e iiceoeaii
?ica’ycaia i?iaeaia ??aiino?.

A i?ae?icae?e? 2.1 ca aeiiiiiaith iecee aeiiii?aeieo oaa?aeaeaiue ie
?icaeaa?ii iia? i?aeoiaee aei aea/aiiy a?oi A?eai?/oea, ye? niieo/athoue
a nia? iiao oai??? iane?i/aiieo a?ioeaaeo aeiaooe?a ne?i/aiieo a?oii oa
iiao ”ia?aeeaaeaiue” i?ae?ioa?aae?a ?ioa?aaeo (0,1).

I?aenoieiaei ?acoeueoaoii i?ae?icae?eo ne?ae aaaaeaoe eaiio 2.1.10,
eio?a aeicaiey? ”cae?aoe” aeaiaioe a?oie A?eai?/oea, ye ae?? ia
?ioa?aae? (0,1), ca aeiiiiiaith iaai?o ae?e ia i?ae?ioa?aaeao.

aoaeooue aai oa??ieie a a?oi? G(,n aai iaeeie/ieie aeaiaioaie.
Iaeiaioa oaea n iacaaii ?aiaii aeaiaioa g ? iicia/eii f(g).

aai anoaiiaeth?oueny, ui oaeiai t a a?oi? G( iaia?, oiaoi aeaiaioe g
oa h ia ? ni?yaeaieie a G(. I?e oeueiio aeaiaio t iiaea aooe aea?aiee c
iaaieie iaiaaeaiiyie.

– aeayea ?aeo?neaia ooieoe?y.

iiaeooue aooe aoaeoeaii ia?a/eneai?.

Iaoiaeeea aea/aiiy a?oi A?eai?/oea, ?icaeiooa a ?iaio? i?e ?ica’ycaii?
i?iaeaie ni?yaeaiino?, aeae? aeei?enoiao?oueny i?e ?icaeyae? ?ioeo
caaea/.

Aea? a?oie noi??i?, yeui aiie iathoue ?ciii?oi? i?aea?oie ne?i/aiiiai
?iaeaena.

A i?ae?icae?e? 2.3 ca aeiiiiiaith eiia?iaoi?ieo i??eoaaiue iienaii c
oi/i?noth aei noi??iino? eiiooaioe a?oi A?eai?/oea, a a ?icae?eao
3.1–3.2 aea/a?oueny iiaaae?iea ooieoe?? ?inoo ia??iae?a oeeo a?oi.

.

Ooieoe?y ?inoo ia??iae?a a a?oiao G(

aia?oa ?icaeyiooa a ?iaio? ?. ?. A?eai?/oea 6, aea anoaiiaeaii ioe?ieo
caa?oo

(1)

aeey ii/aoeiai? a?oie A?eai?/oea Gr.

A ?icae?e? 3.1 ioe?iea Eenueiiea iioe?th?oueny ia oe?oee eean 2-a?oi
A?eai?/oea.

.

Aeey aeiaaaeaiiy oe??? oai?aie ?aeo?aioii aoaeo?oueny aeayea
iane?i/aiia iiiaeeia aeaiaio?a a?oie A?eai?/oea, yea ia? ?yae
aeno?aiaeueieo aeanoeainoae. Cie?aia, aeaiaioe oe??? iiiaeeie iathoue
”iaeo” aeiaaeeio ? ”aaeeeee” ii?yaeie uiaei ?ioeo nai?o ia?aiao??a.

, ie ia?ii

Iniiaiei ia’?eoii i?e ioe?ioe? caa?oo ? ooieoe?y

oaeoe/ii ? ?ioei aeiaaaeaiiyi ioe?iee cieco aeey ?inoo a?oie G(:

(2)

io?eiaiiai a 6. Aa?oi caoaaaeeoe, ui ?. ?. A?eai?/oe iaa?oiooaaa ioe?ieo
(2) aeey aoaeue-yei? ne?i/aiii ii?iaeaeaii? ?aceaeoaeueii ne?i/aiii?
a?oie G ?ioeie iaoiaeaie 14, a naia a oa?i?iao c?inoaiiy eiao?oe??io?a
?yaeo A?eueaa?oa–Ioaiea?a

14 A?eai?/oe ?. E. I ?yaea Aeeueaa?oa-Ioaiea?a a?aaeoe?iaaiiuo
aeaaa?, annioeee?iaaiiuo n a?oiiaie // Iaoai. na. 1989. O. 180. ?2. N.
207–225.

a?aaeoeiaaii? aeaaa?e, iia’ycaii? c a?oiith G. (aeei?enoiaoth/e a?aeii?
?acoeueoaoe Aieiaea–Oaoa?aae/a 15).

?aeay ioe?iee caa?oo ooieoe?? c?inoaiiy ia??iae?a
ne?i/aiii-ii?iaeaeaii? ?aceaeoaeueii ne?i/aiii? a?oie iiaea aeyaeoenue
ei?eniith ? i?e iiooeia? iiaeo ia??iaee/ieo ?aceaeoaeueii ne?i/aiieo
a?oi. Iai?ee?ioe? ?icae?eo 3.2 iaaaaeaii i?inoee i?eeeaae iane?i/aiii?
2-ii?iaeaeaii? {2,3}-a?oie.

aeaiaio?a a?oie G(, ye? ia ia?anoaaeythoue ?ioa?aaee ??aiy m F n i?ae
niaith, ? i?aea?oiith, yeo iaceaathoue noaa?e?caoi?ii ??aiy n.
Aecia/eii einoaa?e?caoi? ??aiy n oaeei /eiii:

?ic?iaeaio a ?iaio? oaoi?eo aeey aeine?aeaeaiue a?oi A?eai?/oea iiaeia
ia?aianoe ia ?io? ?aceaeoaeueii ne?i/aii? a?oie. Aeey aeia?eueii? a?oie
G, yea ae?? ia eieaeueii ne?i/aiiiio ei?aiaaiio aea?aa? i?e?iaeii
aecia/a?oueny ?? ae?y ca aeiiiiiaith ia?aeeaaeaiue i?ae?ioa?aae?a ia
?ioa?aae? (0,1). A oe?e neooaoe?? aiaeiae/ii aaiaeyoueny iiiyooy
noaa?e?caoi?a oa einoaa?e?caoi?a ??ai?a.

Ca nai?ie aeanoeainoyie aeecueeeie aei a?oi A?eai?/oea ? iauiaeaaii
aaaaeai? ?icaaeoaeoaaeuei? a?oie aaoiii?o?ci?a ei?aiaaiai aea?aaa16.
O?ioe ia?aoi?ioethaaaoe i?ea?iaeueia icia/aiiy iiaeia aaaaeaoe ?o
a?oiaie c iane?i/aiiei einoaa?e?caoi?ii eiaeiiai ??aiy. Oe? a?oie,
cie?aia, a?ae?a?athoue aaaeeeao ?ieue i?e aeine?aeaeaii? o. ca.
aeno?aiaeueieo a?oi. A?oia iaceaa?oueny aeno?aiaeueiith, yeui eiaeia ??
aeania oaeoi?-a?oia ne?i/aiia. Caaea/a eeaneo?eaoe?? aeno?aiaeueieo a?oi
cia/iith i??ith caiaeeoueny aei aea/aiiy ?icaaeoaeoaaeueieo
aeno?aiaeueieo a?oi.

15 Aieiae A. N., Oaoa?aae/ E. ?. I aaoia iieae eeannia // Eca. AI
NNN?. Na?. iaoai. O. 28. 1964. N. 261–272.

16 A?eai?/oe ?. E. Ia yeno?aiaeueiuo e aaoayueony a?oiiao // Kurosh
Alg. Conf. 1998. Moscow. P. 163–165.

Iaeia c oe?eaaeo aeanoeainoae ?icaaeoaeoaaeueieo a?oi aea?oueny oaeei
oaa?aeaeaiiyi.

OAI?AIA 3.3.1. Iaoae G o?aiceoeaia a?oia aaoiii?o?ci?a eieaeueii
ne?i/aiiiai ei?aiaaiai aea?aaa c iane?i/aiieie einoaa?e?caoi?aie an?o
??ai?a. Oiae? a G iaia? iao?ea?aeueieo oioiaeiinoae.

I?e aeiaaaeaii? oai?aie ie aeei?enoiao?ii iiiyooy ocaaaeueiaiiai
i?iaeooaaiiy aeaiaio?a, yea c’yaeeinue a ?icae?eao 1–3 aeey a?oi
A?eai?/oea.

Aeno?aiaeueia a?oia iaceaa?oueny niaaeeiai aeno?aiaeueiith16, yeui
eiaeia ?? i?aea?oia ne?i/aiiiai ?iaeaeno aeno?aiaeueia.

. Oaa?aeaeaiiy 3.3.5. aeno?aiaeuei? o?aiceoeai? a?oie
aaoiii?o?ci?a aea?aa c oiiaith iaeneiaeueiino? ? niaaeeiai
aeno?aiaeueieie.

AENIIAEE

A aeena?oaoe?ei?e ?iaio? i?iiiio?oueny iiaee i?aeo?ae aei aea/aiiy
a?oi A?eai?/oea oa a?oi noiaei? eiino?oeoe??. Caaaeyee ii?aeiaiith
??cieo iia aeey aeine?aeaeaiiy aaea?oueny aeae? caaeeaeoenue o aea/aiiy
no?oeoo?e aeaiaio?a a?oi A?eai?/oea.

Oea aeicaieeei iiai?noth ?ica’ycaoe i?iaeaio ni?yaeaiino? a oeeo
a?oiao, a?eueo oi/ii aeine?aeeoe ooieoe?th ?inoo ia??iae?a aeey eiaeii?
c ieo, aeiaanoe oai?aie i?i aoaeiao eiiooaio?a a a?oiao A?eai?/oea, i?i
?o i?ine?i/aiia caieeaiiy, iiaoaeoaaoe iia? i?eeeaaee ia??iaee/ieo a?oi
aa?inaeaeiaiai oeio.

Iaoiaeeea aeine?aeaeaiue, ?icaeiooa a iiaeai?e ?iaio? iiaea aooe
ia?aianaii ? ia ?io? ?aceaeoaeueii ne?i/aii? a?oie, ui a?aeii aaea i?e
aeine?aeaeaii? oioiaeiinoae a ne?i/aiii ii?iaeaeaieo ?aceaeoaeueii
ne?i/aiieo a?oiao. Aaoi? aeneiaeth? ue?o aaey/i?noue nai?io iaoeiaiio
ea??aieeia? i?ioani?ia? A. ?. Nouaineiio ca oaaao ? i?aeo?eieo a
?iaio?.

?IAIOE AAOI?A CA OAIITH AeENA?OAOe??

Eaiiia TH. A. I ooieoeee ?inoa ia?eiaeia a a?oiiao A?eai?/oea // Oacenu
iaaeae. aea. eiio. Neaayine. 1997. N. 56-57.

Eaiiia TH. A. Ieaeiyy ioeaiea ooieoeee ?inoa ia?eiaeia a a?oiiao
A?eai?/oea // Iaoai. nooae??. 1997. O. 8. ?2. N. 192–197.

Eaiiia TH. A. I?i oioiaeiino? a a?oiao aaoiii?o?ci?a aea?aa //A?ni.
Ee?anueeiai Oi-oo. Na?. o?c-iao. 1997. Aei. 3. N. 37–44.

Leonov Yu. G. On identities in branch groups // Abstr. Kurosh Alg.
Conf. 1998. Moscow. P. 77.

Leonov Yu. G. About structure of Grigorchuk groups // Abstr. Int. Conf.
Group and Group Rings VI. Wisla. Poland. 1998, P. 20.

Leonov Yu. G. On growth function for some torsion residually finite
groups // Abstr. Pontrjagin Int. Math. Conf. Moscow. 1998. P. 36–38.

Leonov Yu. G. On precisement of estimation of periods’ growth for
Grigorchuk’s 2- groups // Aii?inu aeaaa?u. 1998. aui. 13. N. 58–67.

Eaiiia TH. A. I?iaeaia nii?yaeaiiinoe a iaeiii eeanna 2-a?oii // Iaoai.
caiaoee. 1998. O. 64. aui. 4. N. 573–583.

Eaiiia TH. A. I?iaeaia ni?yaeaiino? oa ??no ia??iae?a o a?oiao
A?eai?/oea. – ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.01.06 – aeaaa?a ? oai??y
/enae. – Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea, i. Ee?a, 1998.

A aeena?oaoe?? aea/a?oueny 2-a?oie A?eai?/oea oa aeaye? ?io?
ne?i/aiii-ii?iaeaeai? ?aceaeoaeueii ne?i/aii? a?oie iiae?aii?
eiino?oeoe??. I?iiiio?oueny iaaia iaoiaeeea io?eiaiiy ?ioi?iaoe?? i?i
no?oeoo?o aeaiaio?a a a?oiao A?eai?/oea. Cie?aia, iiai?noth
?ica’yco?oueny i?iaeaia ni?yaeaiino? aeaiaio?a a a?oiao A?eai?/oea;
iiaeathoueny ieaeiy oa aa?oiy ioe?iee c?inoaiiy ia??iae?a a 2-a?oiao
A?eai?/oea.

Aaeeiee i?aeo?ae aei aea/aiiy an?o a?oi A?eai?/oea aeicaiey? oaeiae
?icoe?eoe eean a?oi ui aeine?aeaeothoueny: ciaeaeaii iaiao?aei? oiiae
iayaiino? oioiaeiinoae aeey ne?i/aiii-ii?iaeaeaieo ?aceaeoaeueii
ne?i/aiieo a?oi, c yeeo aeieeaa? a?aenooi?noue oioiaeiinoae a a?oiao
A?eai?/oea.

Eeth/ia? neiaa: ia??iaee/ia a?oia, ?aceaeoaeueia ne?i/aiia a?oia,
i?iaeaia ni?yaeaiino?, ooieoe?y ?inoo ia??iae?a a?oie, oioiaeiino? a
a?oiao.

Eaiiia TH. A. I?iaeaia nii?yaeaiiinoe e ?ino ia?eiaeia a a?oiiao
A?eai?/oea.– ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.01.06 – aeaaa?a e
oai?ey /enae. – Eeaaneee oieaa?neoao eiaie Oa?ana Oaa/aiei, a. Eeaa,
1998.

A aeenna?oaoeee eco/athony 2–a?oiiu A?eai?/oea e iaeioi?ua ae?oaea
eiia/ii-ii?iaeaeaiiua oeieoii aii?ieneie?oaiua a?oiiu iioiaeae
eiino?oeoeee. I?aaeeaaaaony ii?aaeaeaiiay iaoiaeeea iieo/aiey
eioi?iaoeee i no?oeoo?a yeaiaioia a a?oiiao A?eai?/oea. A /anoiinoe,
iieiinoueth ?aoaaony i?iaeaia nii?yaeaiiinoe yeaiaioia a a?oiiao
A?eai?/oea; onoaiaaeeaathony ieaeiea e aa?oiea ioeaiee ?inoa ia?eiaeia a
2–a?oiiao A?eai?/oea.

Iauee iiaeoiae i?e eco/aiee anao a?oii A?eai?/oea iicaieyao oaeaea
?anoe?eoue eeann a?oii eioi?ua enneaaeothony: iaeaeaiu iaiaoiaeeiua
oneiaey nouanoaiaaiey oiaeaeanoa aeey eiia/ii-ii?iaeaeaiiuo oeieoii
aii?ieneie?oaiuo a?oii, ec eioi?uo neaaeoao ionoonoaea oiaeaeanoa a
a?oiiao A?eai?/oea.

Eeth/aaua neiaa: ia?eiaee/aneay a?oiia, oeieoii aii?ieneie?oaiay
a?oiia, i?iaeaiia nii?yaeaiiinoe, ooieoeey ?inoa ia?eiaeia a?oiiu,
oiaeaeanoaa a a?oiiao.

Leonov Yu. G. The problem of conjugation and period’s growth in
Grigorchuk’s groups. – Manuscript.

Thesis of dissertation for obtaining the degree of candidate of
sciences in physics and mathematics, speciality 01.01.06 – algebra and
number theory. – Kyiv Taras Shevchenko University, Kyiv, 1998.

In the dissertation work we investigate Grigorchuk’s 2-groups and
some other finite generated residually finite groups of same
construction. We suggest certain procedure for obtaining information
about structure of elements in Grigorchuk’s groups. In particular, we
completely solve conjugace problem of elements in Grigorchuk’s groups;
we establish lower and upper estimation for period’s growth in 2-groups
of Grigorchuk.

Common approach during investigation of all Grigorchuk’s groups
allows expanding the class of groups that are investigated: we obtain
necessary conditions for existing of identities in finite generated
residually finite groups from which follows that there is no identities
in Grigorchuk’s groups.

Key words: torsion group, residually finite group, the conjagace
problem, function of period’s growth for group, identities in groups.

PAGE 16

Похожие записи