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Forum Mathematicum

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Volume 27, Issue 2


Near abelian profinite groups

Karl H. Hofmann / Francesco G. Russo
  • DIEETCAM, Universitá degli Studi di Palermo, Viale Delle Scienze, Edificio 8, 90128, Palermo, Italy. Current address: Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X1, Rondebosch 7701, South Africa
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Published Online: 2012-12-15 | DOI: https://doi.org/10.1515/forum-2012-0125


A compact p-group G (p prime) is called near abelian if it contains an abelian normal subgroup A such that G/A has a dense cyclic subgroup and that every closed subgroup of A is normal in G. We relate near abelian groups to a class of compact groups, which are rich in permuting subgroups. A compact group is called quasihamiltonian (or modular) if every pair of compact subgroups commutes setwise. We show that for p ≠ 2 a compact p-group G is near abelian if and only if it is quasihamiltonian. The case p = 2 is discussed separately.

Keywords: Quasihamiltonian compact groups; hamiltonian compact groups; modular compact groups; monothetic groups; p-adic integers; projective cover

MSC: 22A05; 22A26; 20E34; 20K35

About the article

Received: 2012-08-22

Revised: 2012-09-20

Published Online: 2012-12-15

Published in Print: 2015-03-01

Funding Source: Universitá degli Studi di Palermo

Award identifier / Grant number: “Ex 60 % fondi di internazionalizzazione di ateneo”

Funding Source: GNSAGA (Firenze, Italy)

Award identifier / Grant number: travel support

Citation Information: Forum Mathematicum, Volume 27, Issue 2, Pages 647–698, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0125.

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