论有限群的精确因式分解数

arXiv - MATH - Group Theory Pub Date : 2024-09-16 DOI:arxiv-2409.10428

Jesús Alonso Ochoa Arango, María Angélica Umbarila Martín

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引用次数: 0

摘要

在这项工作中，我们研究了计算有限群 $G$ 的精确因子化次数的函数 $f_2(G)$。我们计算了一些众所周知的有限群族的 $f_2(G)$，并利用维戈尔德和威廉姆森的结果推导出交替群 $A_{2^n}$ 的精确因子化次数的渐近表达式。最后，我们提出了几个关于函数 $f_2(G)$ 的问题，这些问题可能会引起进一步研究的兴趣。

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On the number of exact factorization of finite Groups

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.

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arXiv - MATH - Group Theory

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