Centralizers of abelian subgroups in locally finite simple groups

Download

index.pdf

Date

1997-06-01

Author

Kuzucuoğlu, Mahmut

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

162
views

0
downloads

It is shown that, if a non-linear locally finite simple group is a union of finite simple groups, then the centralizer of every element of odd order has a series of finite length with factors which are either locally solvable or non-abelian simple. Moreover, at least one of the factors is non-linear simple. This is also extended to abelian subgroup of odd orders.

Subject Keywords

Abelian, Centralizers

URI

https://hdl.handle.net/11511/32891

Journal

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY

DOI

https://doi.org/10.1017/s001309150002366x

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Centralizers of involutions in locally finite-simple groups Berkman, A.; Kuzucuoğlu, Mahmut; OeZyurt, E. (2007-01-01) We consider infinite locally finite-simple groups (that is, infinite groups in which every finite subset lies in a finite simple subgroup). We first prove that in such groups, centralizers of involutions either are soluble or involve an infinite simple group, and we conclude that in either case centralizers of involutions are not inert subgroups. We also show that in such groups, the centralizer of an involution is linear if and only if the ambient group is linear.
Centralizers of finite subgroups in simple locally finite groups Ersoy, Kıvanç; Kuzucuoğlu, Mahmut; Department of Mathematics (2009) A group G is called locally finite if every finitely generated subgroup of G is finite. In this thesis we study the centralizers of subgroups in simple locally finite groups. Hartley proved that in a linear simple locally finite group, the fixed point of every semisimple automorphism contains infinitely many elements of distinct prime orders. In the first part of this thesis, centralizers of finite abelian subgroups of linear simple locally finite groups are studied and the following result is proved: If G ...
Centralizers of subgroups in simple locally finite groups ERSOY, KIVANÇ; Kuzucuoğlu, Mahmut (2012-01-01) Hartley asked the following question: Is the centralizer of every finite subgroup in a simple non-linear locally finite group infinite? We answer a stronger version of this question for finite K-semisimple subgroups. Namely let G be a non-linear simple locally finite group which has a Kegel sequence K = {(G(i), 1) : i is an element of N} consisting of finite simple subgroups. Then for any finite subgroup F consisting of K-semisimple elements in G, the centralizer C-G(F) has an infinite abelian subgroup A is...
Centralizers of Finite p-Subgroups in Simple Locally Finite Groups Kuzucuoğlu, Mahmut (Siberian Federal University, 2017-01-01) We are interested in the following questions of B. Hartley: (1) Is it true that, in an infinite, simple locally finite group, if the centralizer of a finite subgroup is linear, then G is linear? (2) For a finite subgroup F of a non-linear simple locally finite group is the order vertical bar CG(F)vertical bar infinite? We prove the following: Let G be a non-linear simple locally finite group which has a Kegel sequence K = {(G(i), 1) : i is an element of N} consisting of finite simple subgroups. Let p be a f...
Centralizers in Hall’s universal groups and direct limits of finitary symmetric groups kegel, Otto; Kuzucuoğlu, Mahmut (2014-01-01) We study the centralizers of finite subgroups in Hall's universal group. We describe the structure of the centralizers of arbitrary finite subgroups in the groups S(\xi) and FSym(\kappa)(\xi) where S(\xi)'s are obtained as direct limits of finite symmetric groups and FSym(\kappa)(\xi)'s are obtained as direct limits of finitary symmetric groups on the set of infinite cardinality \kappa.

Citation Formats

M. Kuzucuoğlu, “Centralizers of abelian subgroups in locally finite simple groups,” PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, pp. 217–225, 1997, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32891.