How many elements are needed to generate a finite group with good probability?

DOI10.1007/BF02784504zbMath1042.20046OpenAlexW1992076965MaRDI QIDQ1860697

Fiorenza Morini, Eloisa Detomi, Andrea Lucchini

Publication date: 2002

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

Full work available at URL: https://doi.org/10.1007/bf02784504

zbMATH Keywords

finite groupspermutation groupsnumbers of generatorscompletely reducible linear groupsrandomly chosen elements

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Generators, relations, and presentations of groups (20F05) Asymptotic results on counting functions for algebraic and topological structures (11N45) Subgroups of symmetric groups (20B35) Probabilistic methods in group theory (20P05)

Related Items (3)

Crowns and factorization of the probabilistic zeta function of a finite group. ⋮ Random generation of associative algebras ⋮ The expected number of random elements to generate a finite group.

Cites Work

• Some applications of the first cohomology group
• Die Eulersche Funktion endlicher auflösbarer Gruppen
• Chains of subgroups in symmetric groups
• The probability of generating a finite classical group
• Zu einem von B. H. und H. Neumann gestellten Problem
• Generating Finite Completely Reducible Linear Groups
• On the number of generators and composition length of finite linear groups

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