CENTRALIZERS IN SIMPLE LOCALLY FINITE GROUPS

This is a survey article on centralizers of finite subgroups in locally finite, simple groups orlfs-groups as we will call them. we mention some of the open problems about centralizers of subgroupsin lfs-groups and applications of the known information about the centralizers of subgroups to thestructure of the locally finite group. we also prove the following: let g be a countably infinite nonlinearlfs-group with a kegel sequence k = f(gi;ni) j i 2 n g. if there exists an upper bound forfjnij j i 2 n g, then for any finite semisimple subgroup f in g the subgroup cg(f) has elements oforder pi for infinitely many distinct prime pi. in particular cg(f) is an infinite group. this answershartley's question provided that there exists a bound on fjnij j i 2 n g: