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

TL;DR

This paper constructs a permutation group that contains exponentially many non-conjugated regular elementary abelian subgroups of order p^3, providing the first such example with exponential growth.

Contribution

It introduces a new family of permutation groups with exponentially many non-conjugated regular elementary abelian subgroups, a novel finding in group theory.

Findings

Constructed permutation groups with at least p^{p-2} non-conjugated subgroups

First example of a permutation group with exponentially many non-conjugated regular subgroups

Demonstrates exponential growth in the number of such 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.