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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

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Volume 16, Issue 1


Classifications of countably-based abelian profinite groups

Jonathan A. Kiehlmann
Published Online: 2013-01-03 | DOI: https://doi.org/10.1515/jgt-2012-0024


In the first half of this paper, we outline the construction of a new class of abelian pro-p groups, which covers all countably-based pro-p groups. In the second half, we study these groups, and classify them up to topological isomorphism and abstract isomorphism. Topologically, any infinitely-generated abelian pro-p group decomposes as a product of infinitely many non-trivial groups. It emerges that they are all abstractly isomorphic to Cartesian products of finite groups and p-adic integers. We have thus constructed uncountably many pairwise topologically non-isomorphic profinite groups abstractly isomorphic to a Cartesian product of cyclic groups.

About the article

Received: 2012-01-20

Revised: 2012-07-16

Published Online: 2013-01-03

Published in Print: 2013-01-01

Citation Information: Journal of Group Theory, Volume 16, Issue 1, Pages 141–157, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt-2012-0024.

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© 2013 by Walter de Gruyter Berlin Boston.Get Permission

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