Let Alt be the alternating group of degree . In this paper we prove that the order complex of the coset poset of Alt is non-contractible for a big family of , including the numbers of the form where and . In order to prove this result, we show that does not vanish, where is the Dirichlet polynomial associated to the group . Moreover, we extend the result to some monolithic primitive groups whose socle is a direct product of alternating groups.
Cite this article
Massimiliano Patassini, On the (non-)Contractibility of the Order Complex of the Coset Poset of an Alternating Group. Rend. Sem. Mat. Univ. Padova 129 (2013), pp. 35–46DOI 10.4171/RSMUP/129-3