Group algebras of generalized primary groups

A number of the known results concerning group algebras of primary groups carry over to group algebras of generalized primary groups. In particular, we show that the group algebra $LG$ of a generalized primary (relative to the prime $p$) group $G$ over the ring $L$, in which the element $p$ is not invertible, determines, to within an isomorphism, a basis subgroup of the generalized primary group $G$. In addition, we indicate two classes of composite abelian groups which are determined, to within an isomorphism, by their group algebras over the ring $L$.