Abstract
Let F be an infinite field of characteristic different from 2 and G a torsion group. Let the group ring FG have an involution induced from an involution on G. We survey recent results establishing the conditions under which the unit group of FG satisfies a *-group identity. The surprising outcome is that the unit group satisfies a *-group identity if and only if the symmetric units of FG satisfy a group identity.
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Communicated by S. Sehgal.