Strongly generating elements in finite and profinite groups

2022/08/11 by Eloisa Detomi, Detomi, Eloisa, Andrea Lucchini +1
Mathematics · Engineering · Computer Science · #Finite Group Theory Research #graph theory and CDMA systems #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2208.05761

Abstract

Given a finite group G and an element g∈ G, we may compare the expected number e(G) of elements needed to generate G and the expected number e(G,g) of elements of G needed to generate G together with g. We address the following question: how large can the difference e(G)-e(G,g) be?

Related

• The probability of generating finite and profinite groups
• Invariable generation and the chebotarev invariant of a finite group
• The expected number of elements to generate a finite group with d-generated Sylow subgroups
• Exponent and number of generators in a finite group
• Flexibility in generating sets of finite groups