Centralizers of finite dimensional elements in unitary groups

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1998

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Çıplak, Murat

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https://hdl.handle.net/11511/1717

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Graduate School of Natural and Applied Sciences, Thesis

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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 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 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 elements in locally finite simple groups. Sezer, Sezgin; Kuzucuoğlu, Mahmut; Department of Mathematics (1992)

Citation Formats

M. Çıplak, “Centralizers of finite dimensional elements in unitary groups,” Middle East Technical University, 1998.