On the number of exact factorization of finite Groups

Jesús Alonso Ochoa Arango; María Angélica Umbarila Martín

paper

On the number of exact factorization of finite Groups

arXiv:2409.10428

Abstract

In this work, we study the function $f_{2} (G)$ that counts the number of exact factorizations of a finite group $G$ . We compute $f_{2} (G)$ for some well-known families of finite groups and use the results of Wiegold and Williamson \cite{WW} to derive an asymptotic expression for the number of exact factorizations of the alternating group $A_{2^{n}}$ . Finally, we propose several questions about the function $f_{2} (G)$ that may be of interest for further research.

19 pages