A note on cyclic semiregular subgroups of some 2-transitive permutation groups

TL;DR

This paper classifies semi-regular subgroups within certain 2-transitive permutation groups, expanding understanding of their subgroup structures in algebraic group theory.

Contribution

It identifies and characterizes semi-regular subgroups of specific 2-transitive groups, providing new insights into their subgroup configurations.

Findings

Semi-regular subgroups are classified for PGL(2,n), PSL(2,n), PGU(3,n), PSU(3,n), Sz(n), and Ree(n).

Results enhance understanding of subgroup structures in algebraic groups.

Provides explicit descriptions of semi-regular subgroups in these groups.

Abstract

We determine the semi-regular subgroups of the 2-transitive permutation groups PGL(2,n), PSL(2,n), PGU(3,n), PSU(3,n), Sz(n) and Ree(n) with n a suitable power of a prime number p.