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ArticleOriginal scientific text

Title

Almost-Bieberbach groups with prime order holonomy

Authors 1, 1

Affiliations

  1. Katholieke Universiteit Leuven, Campus Kortrijk, Universitaire Campus, B-8500 Kortrijk, Belgium

Abstract

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.

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Fundamenta Mathematicae
1996/151/2
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Pages:
167-176
Main language of publication
English
Received
1995-11-21
Accepted
1996-06-26
Published
1996
Exact and natural sciences