English

Strongly generating elements in finite and profinite groups

Group Theory 2022-08-12 v1

Abstract

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

Cite

@article{arxiv.2208.05761,
  title  = {Strongly generating elements in finite and profinite groups},
  author = {Eloisa Detomi and Andrea Lucchini},
  journal= {arXiv preprint arXiv:2208.05761},
  year   = {2022}
}
R2 v1 2026-06-25T01:38:37.203Z