On the irreducibility of the Dirichlet polynomial of a simple group of Lie type.

DOI10.1007/s11856-011-0119-0zbMath1260.20030OpenAlexW2024075557WikidataQ115377699 ScholiaQ115377699MaRDI QIDQ1758943

Massimiliano Patassini

Publication date: 19 November 2012

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-011-0119-0

zbMATH Keywords

Möbius functioncomposition factorsfinite simple groups of Lie typeDirichlet polynomialsprobabilistic zeta function

Mathematics Subject Classification ID

Special subgroups (Frattini, Fitting, etc.) (20D25) 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 the (non-)contractibility of the order complex of the coset poset of an alternating group. ⋮ Recognizing the characteristic of a simple group of Lie type from its probabilistic zeta function. ⋮ Recognizing the Non-Frattini Abelian Chief Factors of a Finite Group from Its Probabilistic Zeta Function ⋮ 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.

Uses Software

• GAP

Cites Work

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• On Large Zsigmondy Primes
• Linear Groups with Orders Having Certain Large Prime Divisors
• COEFFICIENTS OF THE PROBABILISTIC FUNCTION OF A MONOLITHIC GROUP
• On the Möbius function of a finite group

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