Symmetric units in modular group algebras

Abstract

Let p be a primeG a locally finite p-groupK a commutative ring of characteristic p. The anti-automorphism p ↣ g-1 of G extends linearly to an anti-automorphism a ↣a* of K G. An element a of KG is called symmetric if a* a. In this paper we answer the question: for which G and K do the symmetric units of K G form a multiplicative group.