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

Khukhro, E. I. and Makarenko, N. Yu. and Shumyatsky, P. (2015) Locally finite groups containing a $2$-element with Chernikov centralizer. [MIMS Preprint]

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