Almost-crystallographic groups with many outer automorphisms
作者:
Karel Dekimpe,
Wim Malfait,
期刊:
Communications in Algebra
(Taylor Available online 1995)
卷期:
Volume 23,
issue 8
页码: 3073-3083
ISSN:0092-7872
年代: 1995
DOI:10.1080/00927879508825389
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
Almost-crystallographic groups arise as a natural generalization of the well known crystallographic groups. Automorphisms and outer automorphisms of crystallographic groups were treated in [l] (see also [2]). In [10], we developed a method to describe Aut(E) and Out(E) for an almost-crystallographic groupEin terms of commutative diagrams with calculable entries. Here, we continue this study from a different point of view, namely we search for almost-crystallographic groups admitting many (outer) automorphisms. The aim of this paper is to indicate situations in which we can explicitly construct free abelian groups of (outer) automorphisms. Moreover, in many cases, these groups are normal in the full group of (outer) automorphisms. The results obtained are not only of pure algebraic interest, as it is well known that forK(E, l)-manifolds, Out(E) has a relevant geometrical meaning
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