Generating Sets of Mathieu Groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909183772721152 |
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| author | Brooks, Thomas G. |
| author_facet | Brooks, Thomas G. |
| contents | Julius Whiston calculated the maximum size of an irredundant generating set for $S_n$ and $A_n$ by examination of maximal subgroups. Using analogous considerations, we will compute upper bounds to this value for the first two Mathieu groups, $M_{11}$ and $M_{12}$. Computational results gave explicit irredundant generating sets of $M_{11}$ and $M_{12}$ of size 5 and 6, respectively. Together these give the full results that the maximum size of an irredundant generating set for $M_{11}$ is 5 and for $M_{12}$ it is 6. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17995 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generating Sets of Mathieu Groups Brooks, Thomas G. Group Theory 20D05, 20F05 Julius Whiston calculated the maximum size of an irredundant generating set for $S_n$ and $A_n$ by examination of maximal subgroups. Using analogous considerations, we will compute upper bounds to this value for the first two Mathieu groups, $M_{11}$ and $M_{12}$. Computational results gave explicit irredundant generating sets of $M_{11}$ and $M_{12}$ of size 5 and 6, respectively. Together these give the full results that the maximum size of an irredundant generating set for $M_{11}$ is 5 and for $M_{12}$ it is 6. |
| title | Generating Sets of Mathieu Groups |
| topic | Group Theory 20D05, 20F05 |
| url | https://arxiv.org/abs/2404.17995 |