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manuscripta mathematica

, Volume 96, Issue 4, pp 443–461 | Cite as

Symmetric units and group identities

  • A. Giambruno
  • S. K. Sehgal
  • A. Valenti

Abstract:

In this paper we study rings R with an involution whose symmetric units satisfy a group identity. An important example is given by FG, the group algebra of a group G over a field F; in fact FG has a natural involution induced by setting g?g −1 for all group elements gG. In case of group algebras if F is infinite, charF≠ 2 and G is a torsion group we give a characterization by proving the following: the symmetric units satisfy a group identity if and only if either the group of units satisfies a group identity (and a characterization is known in this case) or char F=p >0 and 1) FG satisfies a polynomial identity, 2) the p-elements of G form a (normal) subgroup P of G and G/P is a Hamiltonian 2-group; 3) G is of bounded exponent 4p s for some s≥ 0.

Mathematics Subject Classification (1991):16U60, 16W10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • A. Giambruno
    • 1
  • S. K. Sehgal
    • 2
  • A. Valenti
    • 3
  1. 1.Dipartimento di Matematica e Applicazioni, Università di Palermo, Via Archirafi 34, I-90123 Palermo, Italy. e-mail: a.giambruno@unipa.itIT
  2. 2.Department of Mathematics, University of Alberta, Edmonton, Canada T6G 2G1. e-mail: s.sehgal@ualberta.caCA
  3. 3.Dipartimento di Matematica e Applicazioni, Università di Palermo, Via Archirafi 34, I-90123 Palermo, Italy. e-mail: avalenti@ipamat.math.unipa.itIT

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