A Construction of Metabelian Groups

Abstract

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.

5 pages; to appear in Archiv der Mathematik

References in corpus (2)

• Submodule Categories of Wild Representation Type
• Bounded Submodules of Modules

Cited by in corpus (1)

• Submodule Categories of Wild Representation Type