  Let p be a prime, K a field of characteristic p, G a locally finite p-group,
KG the group algebra, and V the group of the units of KG with augmentation 1.
The anti-automorphism g\mapsto g^{-1} of G extends linearly to KG; this
extension leaves V setwise invariant, and its restriction to V followed by
v\mapsto v^{-1} lives an automorphism of V. The elements of V fixed by this
automorphism are called unitary; they form a subgroup. Our first theorem
describes the K and G for which this subgroup is normal in V.
  For each element g in G, let \bar{g} denote the sum (in KG) of the distinct
powers of g. The elements 1+(g-1)h\bar{g} with g,h\in G are the bicyclic units
of KG. Our second theorem describes the K and G for which all bicyclic units
are unitary.
