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Centralizers of abelian subgroups in locally finite simple groups
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Date
1997-06-01
Author
Kuzucuoğlu, Mahmut
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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
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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 ...
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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.