Higher generating subgroups and Cohen-Macaulay complexes

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).

9 pages; v2: added homological versions of results concerning CM complexes; v3: final version, to appear in Proceedings of the Edinburgh Mathematical Society