Locally finite groups containing a $2$-element with Chernikov centralizer

Abstract

Suppose that a locally finite group $G$ has a $2$-element $g$ with Chernikov centralizer. It is proved that if the involution in $⟨g⟩$ has nilpotent centralizer, then $G$ has a soluble subgroup of finite index.

References in corpus (1)

• Finite groups and Lie rings with an automorphism of order $2^n$