Almost all alternating groups are invariably generated by two elements of prime order

Joni Teräväinen

doi:10.1093/imrn/rnac354

Almost all alternating groups are invariably generated by two elements of prime order

Group Theory 2023-08-24 v2 Number Theory

Authors: Joni Teräväinen

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Abstract

We show that for all $n\leq X$ apart from $O(X\exp(-c(\log X)^{1/2}(\log \log X)^{1/2}))$ exceptions, the alternating group $A_n$ is invariably generated by two elements of prime order. This answers (in a quantitative form) a question of Guralnick, Shareshian and Woodroofe.

Cite

@article{arxiv.2203.05427,
  title  = {Almost all alternating groups are invariably generated by two elements of prime order},
  author = {Joni Teräväinen},
  journal= {arXiv preprint arXiv:2203.05427},
  year   = {2023}
}

Comments

11 pages; Referee comments incorporated; to appear in IMRN

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