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Near abelian profinite groups

Near abelian profinite groups Abstract 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Near abelian profinite groups

Hofmann, Karl H.; Russo, Francesco G.
Forum Mathematicum , Volume 27 (2) – Mar 1, 2015
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Publisher
de Gruyter
Copyright
Copyright © 2015 by the
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2012-0125
Publisher site
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Abstract

Abstract 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.

Journal

Forum Mathematicum – de Gruyter

Published: Mar 1, 2015

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