Expansion of conjugacy classes in PSL(2,q)

TL;DR

This paper investigates the structure of conjugacy classes in PSL(2,q), analyzing their squares, the existence of generating triples with product 1, and the conditions under which elements can be expressed as products of conjugates that generate the group.

Contribution

It provides explicit computations of conjugacy class expansions in PSL(2,q) and characterizes elements as products of conjugates that generate the group, advancing understanding of the group's algebraic structure.

Findings

Computed conjugacy class squares in PSL(2,q)

Identified conditions for triples generating G with product 1

Characterized elements as products of conjugates generating G

Abstract

For any conjugacy class C in G=PSL(2,q) we compute C^2 and discuss whether C contains a triple of elements whose product is 1 which generate G. Moreover, we determine which elements in G can be written as a product of two conjugate elements that generate G.