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Higher generating subgroups and Cohen–Macaulay complexes

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  17 December 2019

Benjamin Brück
Benjamin Brück*
Affiliation:
Bielefeld University, PO Box 10 01 31, D-33501Bielefeld, Germany (benjamin.brueck@uni-bielefeld.de)
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Abstract

We show how to find higher generating families of subgroups, in the sense of Abels and Holz, for groups acting on Cohen–Macaulay complexes. We apply this to groups with a BN-pair to prove higher generation by parabolic and Levi subgroups and describe higher generating families of parabolic subgroups in Aut(Fn).

Keywords

higher generating subgroupsCohen–Macaulay complexesgroups with BN-pairTits buildingsautomorphism groups of free groups

MSC classification

Primary: 20F65: Geometric group theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 1 , February 2020 , pp. 275 - 285
Copyright
Copyright © Edinburgh Mathematical Society 2019

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