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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Isomorphism of commutative group algebras of closed $p$-groups and $p$-local algebraically compact groups
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by Peter Danchev PDF
Proc. Amer. Math. Soc. 130 (2002), 1937-1941 Request permission

Abstract:

Let $G$ be an abelian group and let $K$ be a field of $\mathrm {char} K=p>0$. It is shown via a universal algorithm that if the modified Direct-Factor Problem holds, then the $K$-isomorphism $KH\cong KG$ for some group $H$ yields $H\cong G$ provided $G$ is a closed $p$-group or a $p$-local algebraically compact group. In particular, this is the case when $G$ is closed $p$-primary of arbitrary power, or $G$ is $p$-local algebraically compact with cardinality at most $\aleph _1$ and $K$ is in cardinality not exceeding $\aleph _1$. The last claim completely settles a question raised by W. May in Proc. Amer. Math. Soc. (1979) and partially extends our results published in Rend. Sem. Mat. Univ. Padova (1999) and Southeast Asian Bull. Math. (2001).
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Additional Information
  • Peter Danchev
  • Affiliation: Department of Mathematics, Plovdiv State University, 4000 Plovdiv, Bulgaria – and – Insurance Supervision Directorate, Ministry of Finance, 1000 Sofia, Bulgaria
  • Address at time of publication: 13 General Kutuzov Street, bl. 7, floor 2, flat 4, 4003 Plovdiv, Bulgaria
  • MR Author ID: 346948
  • Email: peter_v@bulstrad.bg, library@math.bas.bg
  • Received by editor(s): May 19, 2000
  • Received by editor(s) in revised form: February 5, 2001
  • Published electronically: February 12, 2002
  • Communicated by: Stephen D. Smith
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 1937-1941
  • MSC (2000): Primary 20C07; Secondary 20K10, 20K20, 20K21
  • DOI: https://doi.org/10.1090/S0002-9939-02-06300-1
  • MathSciNet review: 1896025