Factorizations of simple groups of order 168 and 360
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914643578978304 |
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| author | Kabenyuk, Mikhail |
| author_facet | Kabenyuk, Mikhail |
| contents | A finite group $G$ is called $k$-factorizable if for any factorization $|G|=a_1\cdots a_k$ with $a_i>1$ there exist subsets $A_i$ of $G$ with $|A_i|=a_i$ such that $G=A_1\cdots A_k$. We say that $G$ is \textit{multifold-factorizable} if $G$ is $k$-factorizable for any possible integer $k\geq2$.
We prove that simple groups of orders 168 and 360 are multifold-factorizable and formulate two conjectures that the symmetric group $S_n$ for any $n$ and the alternative group $A_n$ for $n\geq6$ are multifold-factorizable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09306 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Factorizations of simple groups of order 168 and 360 Kabenyuk, Mikhail Group Theory 20B30, 20D40 A finite group $G$ is called $k$-factorizable if for any factorization $|G|=a_1\cdots a_k$ with $a_i>1$ there exist subsets $A_i$ of $G$ with $|A_i|=a_i$ such that $G=A_1\cdots A_k$. We say that $G$ is \textit{multifold-factorizable} if $G$ is $k$-factorizable for any possible integer $k\geq2$. We prove that simple groups of orders 168 and 360 are multifold-factorizable and formulate two conjectures that the symmetric group $S_n$ for any $n$ and the alternative group $A_n$ for $n\geq6$ are multifold-factorizable. |
| title | Factorizations of simple groups of order 168 and 360 |
| topic | Group Theory 20B30, 20D40 |
| url | https://arxiv.org/abs/2401.09306 |