A bound on the expected number of random elements to generate a finite group all of whose Sylow subgroups are d-generated

2016/03/26 by Andrea Lucchini, Lucchini, Andrea
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · Mathematics · #20P05 #Advanced biosensing and bioanalysis techniques #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Nanocluster Synthesis and Applications #math.GR #msc:20P05

paper · pdf · doi:10.48550/arxiv.1603.08098

arxiv created 2016/03/26 · openalex publication_date 2016/03/26 · arxiv updated 2016/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Assume that all the Sylow subgroups of a finite group G can be generated by d elements. Then the expected number of elements of G which have to be drawn at random, with replacement, before a set of generators is found, is at most d+η with η∼ 2.875065.

Related

• The expected number of elements to generate a finite group with d-generated Sylow subgroups
• Probabilistic Bounds on the Number of Elements to Generate Finite Nilpotent Groups and Their Applications
• Probabilistic Generation of Finite Almost Simple Groups
• The Probability of Generating the Symmetric Group
• Bounding the maximal size of independent generating sets of finite groups