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

Aner Shalev
Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel 


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. 


In memory of Brian Hartley