On Bounded Packing in Polycyclic Groups

Abstract

In this paper, we show that any subgroup of a semidirect product of Z^n with Z has bounded packing as long as the action of Z on Z^n is by diagonalizable automorphisms all of whose eigenvalues are real. We use this result to show that any subgroup in a polycyclic group of length 3 or less has bounded packing. We also introduce the notion of coset growth and obtain a bound for the coset growth of subgroup H=<t> in the semidirect product of Z^2 with Z.

References in corpus (2)

• Separable subgroups have bounded packing
• A new proof of Gromov's theorem on groups of polynomial growth

Cited by in corpus (1)

• Separable subgroups have bounded packing