Isomorphism of commutative group algebras of closed -groups and -local algebraically compact groups

Author:
Peter Danchev

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

Published electronically:
February 12, 2002

MathSciNet review:
1896025

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an abelian group and let be a field of . It is shown via a universal algorithm that if the modified *Direct-Factor Problem* holds, then the -isomorphism for some group yields provided is a closed -group or a -local algebraically compact group. In particular, this is the case when is closed -primary of arbitrary power, or is -local algebraically compact with cardinality at most and is in cardinality not exceeding . 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

Email:
peter_v@bulstrad.bg, library@math.bas.bg

DOI:
https://doi.org/10.1090/S0002-9939-02-06300-1

Keywords:
Group algebras,
isomorphism,
closed $p$-groups,
$p$-local algebraically compact groups

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

Article copyright:
© Copyright 2002
American Mathematical Society