On the (non-)contractibility of the order complex of the coset poset of an alternating group.

DOI10.4171/RSMUP/129-3zbMath1281.20027MaRDI QIDQ361733

Massimiliano Patassini

Publication date: 19 August 2013

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

zbMATH Keywords

simplicial complexesorder complexesalternating groupscontractibilityprobabilistic zeta functionsBrown conjecturecoset posets

Mathematics Subject Classification ID

Series and lattices of subgroups (20D30) Other Dirichlet series and zeta functions (11M41) Simple groups: alternating groups and groups of Lie type (20D06) Probabilistic methods in group theory (20P05)

Related Items (2)

Order complexes of coset posets of finite groups are not contractible. ⋮ Boolean lattices in finite alternating and symmetric groups

Cites Work

• Unnamed Item
• On the (non-)contractibility of the order complex of the coset poset of a classical group.
• The probabilistic zeta function of \(\text{PSL}(2,q)\), of the Suzuki groups \(^2B_2(q)\) and of the Ree groups \(^2G_2(q)\).
• Crowns and factorization of the probabilistic zeta function of a finite group.
• On the irreducibility of the Dirichlet polynomial of a simple group of Lie type.
• The coset poset and probabilistic zeta function of a finite group
• Positively finitely generated groups
• Recognizing the Non-Frattini Abelian Chief Factors of a Finite Group from Its Probabilistic Zeta Function
• COEFFICIENTS OF THE PROBABILISTIC FUNCTION OF A MONOLITHIC GROUP

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