On the number of exact factorization of finite Groups

2024/09/16 by Arango, Jesús Alonso Ochoa, Martín, María Angélica Umbarila
#11Z05 #20B05 #20B10 #20B20 #20B30 #20B35 #20D40 #20D60 #20F69 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2409.10428

Abstract

In this work, we study the function f₂(G) that counts the number of exact factorizations of a finite group G. We compute f₂(G) for some well-known families of finite groups and use the results of Wiegold and Williamson \citeWW to derive an asymptotic expression for the number of exact factorizations of the alternating group A_2ⁿ. Finally, we propose several questions about the function f₂(G) that may be of interest for further research.

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