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.
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Received: 8 August 1997
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Giambruno, A., Sehgal, S. & Valenti, A. Symmetric units and group identities . manuscripta math. 96, 443–461 (1998). https://doi.org/10.1007/s002290050076
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DOI: https://doi.org/10.1007/s002290050076