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

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.

arXiv comment6 pages