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Centralizers In Locally Finite Groups, Pavel Shumyatsky

Turkish Journal of Mathematics

The topic of the present paper is the following question. Let G be a locally finite group admitting an automorphism \phi of finite order such that the centralizer C_G(\phi) satisfies certain finiteness conditions. What impact does this have on the structure of the group G? Equivalently, one can ask the same question when \phi is an element of G. Sometimes the impact is quite strong and the paper is a survey of results illustrating this phenomenon. In particular, we concentrate on results where G is shown to have a large nilpotent or soluble subgroup. Naturally, in each case the result …