The structure and topological meaning of almost-torsion free groups

Abstract

n this paper we present a new algebraic characterization of (almost-)crys-tallographic groups. In fact we prove that a virtually abelian (resp. nilpotent) group E is crystallographic (resp. almost-crystallographic) if and only if E has no finite normal subgroups. Thereafter, we investigate more general groups sharing this property and refer to them as the almost-torsion free groups. We show that a virtually polycyclic group Y is almost-torsion free if and only if T is (almost-crystallographic)-by-crystallographic. Thereafter, we take a closer look at the topological properties of almost-torsion free groups.

^ast;Research Assistant National Fund For Scientific Research (Belgium).

^ast;Research Assistant National Fund For Scientific Research (Belgium).

Notes

^ast;Research Assistant National Fund For Scientific Research (Belgium).