Let p be a prime, G a locally finite p-group, K a commutative ring of
characteristic p. The anti-automorphism g bar arrow pointing right g(-
1) of G extends linearly to an anti-automorphism a bar arrow pointing
right a of KG. An element a of KG is called symmetric if a* = a. In t
his paper we answer the question: for which G and K do the symmetric u
nits of KG form a multiplicative group.