Centralizers in residually finite torsion groups

Shalev, Aner

doi:10.1090/S0002-9939-98-04471-2

Centralizers in residually finite torsion groups
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Proc. Amer. Math. Soc. 126 (1998), 3495-3499 Request permission

Abstract:

Let $G$ be a residually finite torsion group. We show that, if $G$ has a finite 2-subgroup whose centralizer is finite, then $G$ is locally finite. We also show that, if $G$ has no $2$-torsion, and $Q$ is a finite 2-group acting on $G$ in such a way that the centralizer $C_G(Q)$ is soluble, or of finite exponent, then $G$ is locally finite.

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