In 1934, Garrett Birkhoff has shown that the number of isomorphism classes of finite metabelian groups of order p22 tends to infinity with p. More precisely, for each prime number p there is a family (Mλ)λ=0,...,p−1 of indecomposable and pairwise nonisomorphic metabelian p-groups of the given order. In this manuscript we use recent results on the classification of possible embeddings of a subgroup in a finite abelian p-group to construct families of indecomposable metabelian groups, indexed by several parameters, which have upper bounds on the exponents of the center and the commutator subgroup.
Mathematics Subject Classification (2000).Primary 20D10 Secondary 20K27 16G60
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