О существовании в группе с конечной инволюцией f-локальных подгрупп

Abstract

An f-local subgroup of an infinite group is each its infinite subgroup with a nontrivial locally finite radical. An involution is said to be finite in a group if it generates a finite subgroup with each conjugate involution. An involution is called isolated if it does not commute with any conjugate involution. We study the group G with a finite non-isolated involution i, which includes infinitely many elements of finite order. It is proved that G has an f-local subgroup containing with i infinitely many elements of finite order. The proof essentially uses the notion of a commuting graph.