Profinite groups with restricted centralizers

Aner Shalev

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

Profinite groups with restricted centralizers

Aner Shalev^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

Let G be a profinite group in which every centralizer C_G(x) (x ϵ G) is either finite or of finite index. It is shown that G is finite-by-abelian-byfinite. 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.

Original language	American English
Pages (from-to)	1279-1284
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	122
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-1994-1239805-3
State	Published - Dec 1994

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title = "Profinite groups with restricted centralizers",

abstract = "Let G be a profinite group in which every centralizer CG(x) (x ϵ G) is either finite or of finite index. It is shown that G is finite-by-abelian-byfinite. 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.",

author = "Aner Shalev",

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N2 - Let G be a profinite group in which every centralizer CG(x) (x ϵ G) is either finite or of finite index. It is shown that G is finite-by-abelian-byfinite. 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.

AB - Let G be a profinite group in which every centralizer CG(x) (x ϵ G) is either finite or of finite index. It is shown that G is finite-by-abelian-byfinite. 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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DO - 10.1090/S0002-9939-1994-1239805-3

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VL - 122

SP - 1279

EP - 1284

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

Profinite groups with restricted centralizers

Abstract

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