A family of permutation groups with exponentially many non-conjugated regular elementary abelian subgroups

Sergei Evdokimov; Mikhail Muzychuk; Ilia Ponomarenko

A family of permutation groups with exponentially many non-conjugated regular elementary abelian subgroups

Group Theory 2021-07-06 v1

Authors: Sergei Evdokimov , Mikhail Muzychuk , Ilia Ponomarenko

Abstract

Given a prime $p$ , we construct a permutation group containing at least $p^{p-2}$ non-conjugated regular elementary abelian subgroups of order $p^3$ . This gives the first example of a permutation group with exponentially many non-conjugated regular subgroups.

Keywords

permutation group regular elementary abelian subgroup non-conjugated subgroups group theory

Cite

@article{arxiv.1609.08467,
  title  = {A family of permutation groups with exponentially many non-conjugated regular elementary abelian subgroups},
  author = {Sergei Evdokimov and Mikhail Muzychuk and Ilia Ponomarenko},
  journal= {arXiv preprint arXiv:1609.08467},
  year   = {2021}
}

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6 pages

A family of permutation groups with exponentially many non-conjugated regular elementary abelian subgroups

Abstract

Keywords

Cite

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