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Embeddings of locally compact abelian p-groups in Hawaiian groups

Embeddings of locally compact abelian p-groups in Hawaiian groups AbstractWe show that locally compact abelian p-groups can be embedded in the first Hawaiian group on a compact path connected subspace of the Euclidean space of dimension four. This result gives a new geometric interpretation for the classification of locally compact abelian groups which are rich in commuting closed subgroups. It is then possible to introduce the idea of an algebraic topology for topologically modular locally compact groups via the geometry of the Hawaiian earring. Among other things, we find applications for locally compact groups which are just noncompact. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Embeddings of locally compact abelian p-groups in Hawaiian groups

Forum Mathematicum , Volume 34 (1): 18 – Jan 1, 2022

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Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2021-0085
Publisher site
See Article on Publisher Site

Abstract

AbstractWe show that locally compact abelian p-groups can be embedded in the first Hawaiian group on a compact path connected subspace of the Euclidean space of dimension four. This result gives a new geometric interpretation for the classification of locally compact abelian groups which are rich in commuting closed subgroups. It is then possible to introduce the idea of an algebraic topology for topologically modular locally compact groups via the geometry of the Hawaiian earring. Among other things, we find applications for locally compact groups which are just noncompact.

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 2022

Keywords: Locally compact abelian groups; Hawaiian earring; homotopy groups; topologically finitely presented groups; 55Q05; 55Q20; 55Q52; 54E45

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