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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
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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?)

  • [GJV] A. Giambruno, E. Jespers and A. Valenti, Group identities on units of rings, Archiv der Mathematik 63 (1994), 291-296. MR 95h:16044
  • [GSV] A. Giambruno, S. K. Sehgal and A. Valenti, Group algebras whose units satisfy a group identity, Proc. AMS, this issue. CMP 96:01
  • [P] D. S. Passman, The Algebraic Structure of Group Rings, Wiley-Interscience, New York, 1977. MR 81d:16001

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Additional Information

D. S. Passman
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

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