ISOMORPHISM CHARACTERIZATION OF DIVISIBLE GROUPS IN MODULAR ABELIAN GROUP RINGS

Suppose G is an abelian group with a p-subgroup H and R is a commutative unitary ring of prime characteristic p with trivial nil-radical. We give a complete description up to isomorphism of the maximal divisible subgroups of 1 + I(RG; H) and (1 + I(RG; H))/H, respectively, where I(RG; H) denotes the relative augmentation ideal of the group algebra RG with respect to H. This paper terminates a series of works by the author on the topic, first of which are [41 and [5].