Products of conjugacy classes of the alternating group

TL;DR

This paper characterizes when the product of two conjugacy classes in the alternating group A_n results in at most four conjugacy classes, providing insights into the structure of these products for n>5.

Contribution

It offers a detailed description of elements in A_n whose conjugacy class products are limited to four or fewer classes, advancing understanding of conjugacy class interactions.

Findings

Identifies conditions for conjugacy class products to have at most four classes

Provides explicit descriptions for such elements in A_n for n>5

Enhances knowledge of the structure of conjugacy class products in alternating groups

Abstract

Let A_n be the alternating group on n letters. For n>5, we describe the elements alpha, beta in A_n when alpha^{A_n} beta^{A_n} is the union of at most four distinct conjugacy classes.