Higher generating subgroups and Cohen-Macaulay complexes
Group Theory
2020-08-07 v3 Combinatorics
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(F_n).
Keywords
Cite
@article{arxiv.1901.04204,
title = {Higher generating subgroups and Cohen-Macaulay complexes},
author = {Benjamin Brück},
journal= {arXiv preprint arXiv:1901.04204},
year = {2020}
}
Comments
9 pages; v2: added homological versions of results concerning CM complexes; v3: final version, to appear in Proceedings of the Edinburgh Mathematical Society