Title: Extensions realizing a faithful abstract kernel and their automorphisms
Authors: Igodt, Paul G. ×
Malfait, Wim #
Issue Date: Aug-1994
Publisher: Springer verlag
Series Title: Manuscripta mathematica vol:84 issue:2 pages:135-161
Abstract: We are interested in group extensions 1 --> N --> E --> F --> 1, for which the corresponding abstract kernel F --> Out(N) is faithful. For these groups E, we develop commutative diagrams which are helpful to understand and to compute Aut(E, N) (the group of all E-automorphisms mapping N into itself) and Out(E, N) = Aut(E, N)/Inn(E). Of course, if N is characteristic in E, Aut(E, N) = Aut(E) and Out(E,N) = Out(E). These conditions occur e.g. when studying almost crystallographic groups, which were in fact the initiating cases to us. Similar work has been done previously by Conner and Raymond ([3]) (several types where N = Z(k)) and by Charlap ([1]) (for crystallographic groups). Although the approach in both works is rather different, we did an effort to obtain a description covering most aspects of both previously developed pictures. We include the results of an example computation for one family of isomorphism types of 3-dimensional almost crystallographic groups. For K(E, 1)-manifolds it is known that Out(E) has an important geometric meaning. In the closing section and for certain K(E, 1)-manifolds, we establish a geometric interpretation of Out(E, N) and its subgroups from the determining diagrams.
ISSN: 0025-2611
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Mathematics, Campus Kulak Kortrijk
× corresponding author
# (joint) last author

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