Centralizers of elements in locally finite simple groups.

Sezer, Sezgin


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 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 involutions in locally finite groups
Kuzucuoğlu, Mahmut (Informa UK Limited, 2007-01-01)
The present article deals with locally finite groups G having an involution phi such that C-G(phi) is an SF-group. It is shown that G possesses a normal subgroup B which is a central product of. nitely many groups isomorphic to PSL(2, K-i) or SL(2, Ki) for some in finite locally finite fields K-i of odd characteristic, such that [G, phi]'/B and G/[G, phi] are both SF-groups.
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 dimensional elements in unitary groups
Çıplak, Murat; Kuzucuoğlu, Mahmut; Department of Mathematics (1998)
Citation Formats
S. Sezer, “Centralizers of elements in locally finite simple groups.,” Middle East Technical University, 1992.