On the (non-)contractibility of the order complex of the coset poset of a classical group.

DOI10.1016/j.jalgebra.2011.05.042zbMath1242.20026OpenAlexW2030884465MaRDI QIDQ661895

Massimiliano Patassini

Publication date: 11 February 2012

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2011.05.042

zbMATH Keywords

simplicial complexesorder complexesclassical groupscontractibilityprobabilistic zeta functionsBrown conjecturecoset posets

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Maximal subgroups (20E28) 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 (4)

Order complexes of coset posets of finite groups are not contractible. ⋮ Order complex of ideals in a commutative ring with identity ⋮ On the (non-)contractibility of the order complex of the coset poset of an alternating group. ⋮ Boolean lattices in finite alternating and symmetric groups

Uses Software

• GAP

Cites Work

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• Endliche Gruppen I
• THE EULERIAN FUNCTIONS OF A GROUP
• On the Möbius function of a finite group

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