Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Peter Danchev
Journal: Proc. Amer. Math. Soc. 130 (2002), 1937-1941
MSC (2000): Primary 20C07; Secondary 20K10, 20K20, 20K21
Published electronically: February 12, 2002
MathSciNet review: 1896025
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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).


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20C07, 20K10, 20K20, 20K21

Retrieve articles in all journals with MSC (2000): 20C07, 20K10, 20K20, 20K21


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: http://dx.doi.org/10.1090/S0002-9939-02-06300-1
PII: S 0002-9939(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