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

Sergei Evdokimov, Mikhail Muzychuk, Ilia Ponomarenko

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 o…