On the Distribution of Values of Certain Word Maps

TL;DR

This paper investigates the behavior of specific word maps on large finite simple groups, showing they nearly preserve measure, which has implications for understanding group structure and word distribution.

Contribution

It demonstrates that the word map (x,y) -> x^m y^n is almost measure preserving on large finite simple groups, extending understanding of word map distributions.

Findings

Word map (x,y) -> x^m y^n is almost measure preserving

Results apply to large finite simple groups

Advances knowledge of word distribution in group theory

Abstract

For any positive integers m and n, the word map (x,y) -> x^m y^n is almost measure preserving on large finite simple groups G.