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.
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- D. S. Passman
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- MR Author ID: 136635
- Email: firstname.lastname@example.org
- Received by editor(s): August 31, 1995
- Additional Notes: This research was supported by NSF Grant DMS-9224662.
- Communicated by: Ronald M. Solomon
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 657-662
- MSC (1991): Primary 16S34
- DOI: https://doi.org/10.1090/S0002-9939-97-04024-0
- MathSciNet review: 1415361