JournalsrsmupVol. 129pp. 35–46

On the (non-)Contractibility of the Order Complex of the Coset Poset of an Alternating Group

  • Massimiliano Patassini

    Vidor (TV), Italy
On the (non-)Contractibility of the Order Complex of the Coset Poset of an Alternating Group cover
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Abstract

Let Alt k_k be the alternating group of degree kk. In this paper we prove that the order complex of the coset poset of Alt k_k is non-contractible for a big family of kNk\in {\mathbb N} , including the numbers of the form k=p+mk=p+m where m{3,,35}m\in \{3,\ldots,35\} and p>k/2p> k/2. In order to prove this result, we show that PG(1)P_G(-1) does not vanish, where PG(s)P_G(s) is the Dirichlet polynomial associated to the group GG. 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. 35–46

DOI 10.4171/RSMUP/129-3