On locally finite groups with a small centralizer of a four-subgroup

被引：3

作者：

Romano, Emanuela ^{[1
]}

Shumyatsky, Pavel ^{[2
]}

机构：

[1] Univ Salerno, Dipartimento Matemat & Informat, I-84084 Fisciano, SA, Italy

[2] Univ Brasilia, Dept Math, BR-70910900 Brasilia, DF, Brazil

来源：

ARCHIV DER MATHEMATIK | 2011年 / 97卷 / 01期

关键词：

Locally finite groups; Centralizers; PERIODIC LINEAR-GROUPS; PRIME-ORDER; SOLUBLE GROUPS; ELEMENT;

D O I：

10.1007/s00013-011-0273-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main result of the paper is the following theorem. Let G be a locally finite group having a four-subgroup V such that C-G(V) is finite. Suppose that V contains two involutions v(1) and v(2) such that the centralizers C-G(v(1)) and C-G(v(2)) have finite exponent. Then G is almost locally soluble and [G, V]' has finite exponent. Since [G, V] has finite index in G, the result gives a fairly detailed information about the structure of G.

引用

页码：1 / 10

页数：10

共 50 条

[1] On locally finite groups with a small centralizer of a four-subgroup
Emanuela Romano
Pavel Shumyatsky
[J]. Archiv der Mathematik, 2011, 97 : 1 - 10
[2] On locally finite groups with a four-subgroup whose centralizer is small
Enio Lima
Pavel Shumyatsky
[J]. Monatshefte für Mathematik, 2013, 172 : 77 - 84
[3] On locally finite groups with a four-subgroup whose centralizer is small
Lima, Enio
Shumyatsky, Pavel
[J]. MONATSHEFTE FUR MATHEMATIK, 2013, 172 (01): : 77 - 84
[4] On groups having a four-subgroup with finite centralizer
Shumyatsky, P
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 1998, 49 (196): : 491 - 499
[5] Locally finite groups of finite centralizer dimension
Borovik, Alexandre
Karhumaki, Ulla
[J]. JOURNAL OF GROUP THEORY, 2019, 22 (04) : 729 - 740
[6] CHARACTERIZATION OF CHERINIKOV GROUPS IN CLASS OF SHUNKOV GROUPS WITH SYLOW FOUR-SUBGROUP
Ivko, M. N.
[J]. SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2006, 3 : 232 - 237
[7] Locally Finite Groups with Bounded Centralizer Chains
Buturlakin, A. A.
Vasil'ev, A. V.
[J]. ALGEBRA AND LOGIC, 2013, 52 (05) : 367 - 370
[8] Locally Finite Groups with Bounded Centralizer Chains
A. A. Buturlakin
A. V. Vasil’ev
[J]. Algebra and Logic, 2013, 52 : 367 - 370
[9] Locally finite groups containing a -element with Chernikov centralizer
Khukhro, E. I.
Makarenko, N. Yu.
Shumyatsky, P.
[J]. MONATSHEFTE FUR MATHEMATIK, 2016, 179 (01): : 91 - 97
[10] On the centralizer of an element of order four in a locally finite group
Shumyatsky, Pavel
[J]. GLASGOW MATHEMATICAL JOURNAL, 2007, 49 : 411 - 415

← 1 2 3 4 5 →