Symmetric units and group identities |
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Authors: | A Giambruno S K Sehgal A Valenti |
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Institution: | (1) Dipartimento di Matematica e Applicazioni, Università di Palermo, Via Archirafi 34, I-90123 Palermo, Italy. e-mail: a.giambruno@unipa.it, IT;(2) Department of Mathematics, University of Alberta, Edmonton, Canada T6G 2G1. e-mail: s.sehgal@ualberta.ca, CA;(3) Dipartimento di Matematica e Applicazioni, Università di Palermo, Via Archirafi 34, I-90123 Palermo, Italy. e-mail: avalenti@ipamat.math.unipa.it, IT |
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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 g∈G. 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.
Received: 8 August 1997 |
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Keywords: | Mathematics Subject Classification (1991):16U60 16W10 |
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