On the Dirichlet polynomial of finite groups of Lie type.

zbMath1167.20334MaRDI QIDQ833476

Andrea Lucchini, Erika Damian

Publication date: 13 August 2009

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

Full work available at URL: https://eudml.org/doc/108685

zbMATH Keywords

finite simple groupsfinite groups of Lie typeprobabilistic zeta functionsirreducible Dirichlet polynomials

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 (6)

On Integers that are Covering Numbers of Groups ⋮ Recognizing the characteristic of a simple group of Lie type from its probabilistic zeta function. ⋮ Covers and normal covers of finite groups. ⋮ On the (non-)contractibility of the order complex of the coset poset of a classical group. ⋮ On the irreducibility of the Dirichlet polynomial of a simple group of Lie type. ⋮ On finite simple groups and Kneser graphs.

Cites Work

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• Homotopy properties of the poset of nontrivial p-subgroups of a group
• The coset poset and probabilistic zeta function of a finite group
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• The maximal factorizations of the finite simple groups and their automorphism groups
• On Large Zsigmondy Primes
• Composition Factors from the Group Ring and Artin's Theorem on Orders of Simple Groups
• RECOGNIZING SOLUBLE GROUPS FROM THEIR PROBABILISTIC ZETA FUNCTIONS
• Linear Groups with Orders Having Certain Large Prime Divisors
• RECOGNIZING THE ALTERNATING GROUPS FROM THEIR PROBABILISTIC ZETA FUNCTION
• The Subgroups of PSL(3, q) for odd q
• Endliche Gruppen I
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