A Construction of Metabelian Groups

Details A Construction of Metabelian Groups A Construction of Metabelian Groups

2004-07-29

arxiv.org/abs/math/0407515v2

Mathematics

Group Theory

5 pages; to appear in Archiv der Mathematik

Scientific paper

In 1934, Garrett Birkhoff has shown that the number of isomorphism classes of finite metabelian groups of order $p^{22}$ tends to infinity with $p$. More precisely, for each prime number $p$ there is a family $(M_\lambda)_{\lambda=0,...,p-1}$ 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.

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