Invariable generation of finite simple groups and rational homology of coset posets

Abstract

We show that every finite simple group is generated invariably by a Sylow subgroup and a cyclic group. It follows that that the order complex of the coset poset of an arbitrary finite group has nontrivial reduced rational homology.

14 pages; v2 has minor changes for publication

References in corpus (3)

• The maximal subgroups of the exceptional groups $F_4(q)$, $E_6(q)$ and ${}^2{E}_6(q)$ and related almost simple groups
• Almost all alternating groups are invariably generated by two elements of prime order
• On invariable generation of alternating groups by elements of prime and prime power order