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)

 

Group algebras whose units satisfy
a group identity. II


Author: D. S. Passman
Journal: Proc. Amer. Math. Soc. 125 (1997), 657-662
MSC (1991): Primary 16S34
MathSciNet review: 1415361
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ K[G]$ be the group algebra of a torsion group $G$ over an infinite field $K$, and let $U=U(G)$ denote its group of units. A recent paper of A. Giambruno, S. K. Sehgal, and A. Valenti proved that if $U$ satisfies a group identity, then $K[G]$ satisfies a polynomial identity, thereby confirming a conjecture of Brian Hartley. Here we add a footnote to their result by showing that the commutator subgroup $G'$ of $G$ must have bounded period. Indeed, this additional fact enables us to obtain necessary and sufficient conditions for $U(G)$ to satisfy an identity.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 16S34

Retrieve articles in all journals with MSC (1991): 16S34


Additional Information

D. S. Passman
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: passman@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04024-0
PII: S 0002-9939(97)04024-0
Received by editor(s): August 31, 1995
Additional Notes: This research was supported by NSF Grant DMS-9224662.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society