On the number of exact factorization of finite Groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910605597736960 |
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| author | Arango, Jesús Alonso Ochoa Martín, María Angélica Umbarila |
| author_facet | Arango, Jesús Alonso Ochoa Martín, María Angélica Umbarila |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the number of exact factorization of finite Groups Arango, Jesús Alonso Ochoa Martín, María Angélica Umbarila Group Theory 20D40, 20D60, 20B05, 20B20, 20B30, 20B35, 20B10, 20F69, 11Z05 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. |
| title | On the number of exact factorization of finite Groups |
| topic | Group Theory 20D40, 20D60, 20B05, 20B20, 20B30, 20B35, 20B10, 20F69, 11Z05 |
| url | https://arxiv.org/abs/2409.10428 |