scientific article; zbMATH DE number 903688
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Publication:4885303
zbMath0853.11075MaRDI QIDQ4885303
Publication date: 9 January 1997
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Zeta and (L)-functions: analytic theory (11M99) Probabilistic theory: distribution modulo (1); metric theory of algorithms (11K99)
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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 ⋮ Crowns and factorization of the probabilistic zeta function of a finite group. ⋮ Recognizing the characteristic of a simple group of Lie type from its probabilistic zeta function. ⋮ The coset poset and probabilistic zeta function of a finite group ⋮ On the (non-)contractibility of the order complex of the coset poset of a classical group. ⋮ Profinite groups in which the probabilistic zeta function coincides with the subgroup zeta function. ⋮ Finiteness of Profinite Groups with a Rational Probabilistic Zeta Function ⋮ On the probabilistic zeta function for finite groups ⋮ Profinite groups in which the probabilistic zeta function has no negative coefficients ⋮ On the irreducibility of the Dirichlet polynomial of an alternating group ⋮ Recognizing \(\mathrm{PSL}(2,p)\) in the non-Frattini chief factors of finite groups.
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