On the theory and classification of Abelianp-groups

Uniqueness theorems for global mixed groups

“…In the local setting, our first lemma is substantially a known result (see, for example, the proof of Theorem 3.2 in [HM1] or the proofof Lemma 2.3 in [HM4]), but the independent proof given below deals with the two essential cases in a more elegant manner than in earlier treatments. G and G', respectively.…”

An isomorphism theorem for commutative modular group algebras

“…Note fn -fn includes equality of the Ulm-Kaplansky invariants fH and fK . Therefore, since H and K are almost balanced subgroups of L, the main theorem in [5] implies H = K. D To see that Theorem 2 actually gives us something new, the following example shows that there exist A2(p)-groups which are not /z-elementary ^4-groups. The reference for the theory of c-valuations used below is [5].…”

“…Such an A may be seen to exist for every a e A . By Theorem 2.8 in [5], there exists a totally projective group G and an isotype subgroup H of G such that G/H = A as c-valuated groups, where the c-valuation on G/H is the coset valuation. It now easily follows that (H, G) is an A2(p)-pair.…”

An isomorphism theorem for group pairs of finite abelian groups

“…Two subgroups A and B of a group G are said to be equivalent if there is an automorphism of G that maps A onto B. The equivalence theory of subgroups is a rapidly emerging subject that plays an important role in the structure of abelian groups; see, for example, [H1], [H2] and [HM1]- [HM4]. A solution to the following problem is a basic goal in the equivalence theory.…”