CONJUGACY CLASSES OF THE GROUP OF UNITS IN GROUP ALGEBRAS OF FINITE p-GROUPS.

Let Fpn G be the group algebra of a finite p-group G over a field FPn with pn elements, and V(FPnG) the subgroup of units of augmentation 1. We investigate the conjugacy classes of V(Pn G), showing that p2n divides the order of the conjugacy class ∣ Ca ∣ for a noncentral element a e Fpn G and V(Fpn G) contains a conjugacy class of order p 2n, if a nonabelian finite p-group G has a factor group G/H such that its centre is of index p2. [ABSTRACT FROM AUTHOR]