On symmetric units in group algebras

Bódi, Viktor (2001) On symmetric units in group algebras. Communications in Algebra, 29 (12). pp. 5411-5422. ISSN 0092-7872 (print), 1532-4125 (online)

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Abstract

Let U(KG) be the group of units of the group ring KG of the group G over a commutative ring K. The anti-automorphism g bar right arrow g(-1) of G can be extended linearly to an anti-automorphism a bar right arrow a* of KG. Let S*(KG) = {x is an element of U(KG) / x* = x} be the set of all symmetric units of U(KG). We consider the following question: for which groups G and commutative rings K it is true that S,(KG) is a subgroup in U(KG). We answer this question when either a) G is torsion and K is a commutative G-favourable integral domain of characteristic p greater than or equal to 0 or b) G is non-torsion nilpotent group and KG is semiprime.

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