Centralizers of Involutions in Locally Finite Groups

Abstract

The present article deals with locally finite groups G having an involution φ such that C _G (φ) is an SF-group. It is shown that G possesses a normal subgroup B which is a central product of finitely many groups isomorphic to PSL(2, K _i ) or SL(2, K _i ) for some infinite locally finite fields K _i of odd characteristic, such that [G, φ]′/B and G/[G, φ] are both SF-groups.

Key Words:

• Centralizers
• Locally finite groups

1991 Mathematics Subject Classification:

• 20E25

ACKNOWLEDGMENTS

Research by the first author was partially supported by the Scientific and Technical Research Council of Turkey. Research by the second author was supported by FINATEC-Brazil.

Notes

Communicated by M. R. Dixon.