The coset poset and probabilistic zeta function of a finite group

DOI10.1006/jabr.1999.8221zbMath0973.20016OpenAlexW2017827867MaRDI QIDQ1972437

K. Stephen Brown

Publication date: 28 August 2001

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

Full work available at URL: https://semanticscholar.org/paper/acad512c6b68677026b5d5a8b1a2bb50af39507f

zbMATH Keywords

finite groupssubgroupscosetsEuler characteristicszeta functionsgeneralized Möbius functions

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Series and lattices of subgroups (20D30) Other Dirichlet series and zeta functions (11M41) Probabilistic methods in group theory (20P05)

Related Items (33)

The A-Möbius function of a finite group ⋮ Subgroup graph methods for presentations of finitely generated groups and the contractibility of associated simplicial complexes ⋮ On the Dirichlet polynomial of finite groups of Lie type. ⋮ The probabilistic zeta function of finite simple groups. ⋮ Order complexes of coset posets of finite groups are not contractible. ⋮ On the (non-)contractibility of the order complex of the coset poset of an alternating group. ⋮ Recognizing a finite group from the generating properties of its subsets ⋮ Shelling the coset poset. ⋮ Crowns and factorization of the probabilistic zeta function of a finite group. ⋮ Between buildings and free factor complexes: A Cohen–Macaulay complex for Out(RAAGs) ⋮ Prefrattini subgroups and crowns ⋮ Higher generating subgroups and Cohen–Macaulay complexes ⋮ On families of nilpotent subgroups and associated coset posets ⋮ Boolean lattices in finite alternating and symmetric groups ⋮ Homotopy types of group lattices ⋮ Ore's theorem on subfactor planar algebras ⋮ On the (non-)contractibility of the order complex of the coset poset of a classical group. ⋮ On Boolean intervals of finite groups ⋮ Strange divisibility in groups and rings ⋮ A PROBABILISTIC GENERALIZATION OF SUBNORMALITY ⋮ On the irreducibility of the Dirichlet polynomial of a simple group of Lie type. ⋮ Finite Groups withp-Multiplicative Probabilistic Zeta Function ⋮ Spherical posets from commuting elements ⋮ COEFFICIENTS OF THE PROBABILISTIC FUNCTION OF A MONOLITHIC GROUP ⋮ Homotopy colimits of classifying spaces of abelian subgroups of a finite group ⋮ On the lattice of subquandles of a Takasaki quandle ⋮ The Probabilistic Zeta Function of Alternating and Symmetric Groups ⋮ On the lattice of subracks of the rack of a finite group ⋮ Profinite groups in which the probabilistic zeta function has no negative coefficients ⋮ ON THE POSET OF NON-TRIVIAL PROPER SUBGROUPS OF A FINITE GROUP ⋮ Coset posets of infinite groups ⋮ Stanley-Reisner rings for symmetric simplicial complexes, \(G\)-semimatroids and abelian arrangements ⋮ Recognizing \(\mathrm{PSL}(2,p)\) in the non-Frattini chief factors of finite groups.

Uses Software

• GAP

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