Profinite groups with restricted centralizers

Shalev, Aner

doi:10.1090/S0002-9939-1994-1239805-3

Profinite groups with restricted centralizers
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Proc. Amer. Math. Soc. 122 (1994), 1279-1284 Request permission

Abstract:

Let G be a profinite group in which every centralizer ${C_G}(x)\;(x \in G)$ is either finite or of finite index. It is shown that G is finite-by-abelian-by-finite. Moreover, if, in addition, G is a just-infinite pro-p group, then it has the structure of a p-adic space group whose point group is cyclic or generalized quaternion.

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