Geodesic
Almost-Bieberbach groups with prime order holonomy
Fundamenta Mathematicae, Tome 151 (1996) no. 2, pp. 167-176.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The main issue of this paper is an attempt to find a decomposition theorem for infra-nilmanifolds in the same spirit as a result of A. Vasquez for flat Riemannian manifolds. That is: we look for infra-nilmanifolds with prime order holonomy which can be obtained as a fiber space with a non-trivial nilmanifold as fiber and an infra-nilmanifold as its base.   In this perspective, we prove the following algebraic result: if E is an almost-Bieberbach group with prime order holonomy, then there is a normal subgroup Π of E contained in the Fitting subgroup of E such that E/Π is an almost-Bieberbach group either having a Fitting subgroup with center isomorphic to the infinite cyclic group, or having an underlying crystallographic group with torsion and a center coinciding with that of its Fitting subgroup.
DOI : 10.4064/fm-151-2-167-176

Karel Dekimpe 1 ; Wim Malfait 1

1 
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Karel Dekimpe; Wim Malfait. Almost-Bieberbach groups with prime order holonomy. Fundamenta Mathematicae, Tome 151 (1996) no. 2, pp. 167-176. doi : 10.4064/fm-151-2-167-176. http://geodesic.mathdoc.fr/articles/10.4064/fm-151-2-167-176/

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