Higher generating subgroups and Cohen-Macaulay complexes

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...

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Bibliographic Details
Published in:arXiv.org 2019-08
Main Author: Brück, Benjamin
Format: Article
Language:English
Subjects:
Subgroups
Online Access:Get full text
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Summary: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(F_n).
ISSN:2331-8422
DOI:10.48550/arxiv.1901.04204