  Let p be a prime, G a locally finite p-group, K a commutative ring of
characteristic p. The anti-automorphism g\mapsto g\m1 of G extends linearly to
an anti-automorphism a\mapsto a^* of KG. 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 KG form a multiplicative group.
