95-7   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Roland Schmidt:

Lattice Embeddings of Abelian Prime Power Groups

We solve the following problem which was posed by D. W. Barnes in 1962. For which abelian groups G and H of the same prime power order is it possible to embed the subgroup lattice of G in that of H? We show that if there exists such an embedding and G contains three independent elements of order p2, then G and H are isomorphic. This reduces the problem to the case that G is the direct product of cyclic p-groups only two of which have order larger than p. We determine all groups H for which the desired embedding exists.

Bibliographical note: J. Austral. Math. Soc. (Series A) 62 (1997), 259 - 278


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