Locally Finite Groups with Centralizers of Finite Rank.

The structure of locally finite groups with an involution whose centralizer has finite rank was described by Kuzucuolu and Shumyatsky. In this paper, we investigate the structure of locally finite groups with an element of order 3 whose centralizer has finite rank. Moreover, for anyp, we classify simple locally finite groups having an automorphism of orderpwhose set of fixed points has finite rank. [ABSTRACT FROM AUTHOR]