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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


Authors: Antonio Giambruno, Sudarshan Sehgal and Angela Valenti
Journal: Proc. Amer. Math. Soc. 125 (1997), 629-634
MSC (1991): Primary 16S34; Secondary 20C05
MathSciNet review: 1350944
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Abstract: Let $FG$ be the group algebra of a torsion group over an infinite field $F$. Let $U$ be the group of units of $FG$. We prove that if $U$ satisfies a group identity, then $FG$ satisfies a polynomial identity. This confirms a conjecture of Brian Hartley.


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Additional Information

Antonio Giambruno
Affiliation: $\mathrm{(A. Giambruno and A. Valenti)}$ Dipartimento di Matematica, Universitá di Palermo, via Archirafi 34, 90123 Palermo, Italy
Email: giambruno@ipamat.math.unipa.it, avalenti@ipamat.math.unipa.it

Sudarshan Sehgal
Affiliation: $\mathrm{(S. Sehgal)}$ Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: ssehgal@schur.math.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03581-8
PII: S 0002-9939(97)03581-8
Received by editor(s): June 26, 1995
Additional Notes: Research supported by NR and MURST of Italy and NSERC of Canada.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society