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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Profinite groups with restricted centralizers

Author: Aner Shalev
Journal: Proc. Amer. Math. Soc. 122 (1994), 1279-1284
MSC: Primary 20E18; Secondary 20F24
MathSciNet review: 1239805
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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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PII: S 0002-9939(1994)1239805-3
Article copyright: © Copyright 1994 American Mathematical Society

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