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Group algebras with symmetric units satisfying a group identity

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Abstract

We study group algebras FG for which the symmetric units under the natural involution: g *=g −1 satisfy a group identity. For infinite fields F of characteristic ≠2, a classification of torsion groups G whose symmetric units U +(FG) satisfy a group identity was given in [3] by Giambruno-Sehgal-Valenti. We extend this work to non torsion groups.

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, T6G 2G1, Edmonton, Canada

    S.K. Sehgal

  2. Dipartimento di Metodi e Modelli Matematici, Università di Palermo, Viale delle Scienze, 90128, Palermo, Italy

    A. Valenti

Authors
  1. S.K. Sehgal
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  2. A. Valenti
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Correspondence to S.K. Sehgal.

Additional information

Research supported by NSERC of Canada and MIUR of Italy.

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Sehgal, S., Valenti, A. Group algebras with symmetric units satisfying a group identity. manuscripta math. 119, 243–254 (2006). https://doi.org/10.1007/s00229-005-0610-1

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  • DOI: https://doi.org/10.1007/s00229-005-0610-1

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