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

E. I. Khukhro; N. Yu. Makarenko; P. Shumyatsky

arxiv: 1410.1521 · v1 · pith:R5X7HO5Gnew · submitted 2014-10-04 · 🧮 math.GR

Locally finite groups containing a 2-element with Chernikov centralizer

E. I. Khukhro , N. Yu. Makarenko , P. Shumyatsky This is my paper

classification 🧮 math.GR

keywords centralizerfinitechernikovelementlocallycontaininggroupgroups

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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.

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Locally finite groups containing a 2-element with Chernikov centralizer

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