Abstract. Let $G$ be a $p$-group and denote by $E(G)$ the set of all elements $g\in\Delta (G)$ such that $g$ has infinite height in the centre of the centralizer $C_G(g)$ of $g$. Under the assumption that $E(G)$ is a subgroup, we describe the first Ulm-subgroup and the maximal divisible subgroup of the centre of the unit group of the group algebra of a $p$-group over a field of characteristic $p$. Every nilpotent and $FC$-group satisfies these properties.

AMS Subject Classification (1991): 16S34, 16U60, 20C07

Keyword(s): group algebra, unit group, divisible group

Received February 14, 1996 and in revised form October 18, 1996. (Registered under 6103/2009.)