CENTRALIZERS OF ABELIAN SUBGROUPS IN LOCALLY FINITE SIMPLE-GROUPS

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