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 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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DOI:
https://doi.org/10.1090/S0002-9939-1994-1239805-3

Article copyright:
© Copyright 1994
American Mathematical Society