Centralizers of abelian subgroups in locally finite simple groups

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Kuzucuoglu M.

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, vol.40, pp.217-225, 1997 (SCI-Expanded) identifier identifier


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.