Conjugate generation of sporadic almost simple groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918054324076544 |
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| author | Revin, Danila O. Zavarnitsine, Andrei V. |
| author_facet | Revin, Danila O. Zavarnitsine, Andrei V. |
| contents | As defined by Guralnick and Saxl, given a nonabelian simple group $S$ and its nonidentity automorphism $x$, a natural number $α_S(x)$ is the minimum number of conjugates of $x$ in $\langle x,S\rangle$ that generate a subgroup containing $S$. In this paper, for every sporadic group $S$ other than the Monster and an automorphism $x$ of $S$ of prime order, we complete the determination of the precise value of $α_S(x)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conjugate generation of sporadic almost simple groups Revin, Danila O. Zavarnitsine, Andrei V. Group Theory 20D08 As defined by Guralnick and Saxl, given a nonabelian simple group $S$ and its nonidentity automorphism $x$, a natural number $α_S(x)$ is the minimum number of conjugates of $x$ in $\langle x,S\rangle$ that generate a subgroup containing $S$. In this paper, for every sporadic group $S$ other than the Monster and an automorphism $x$ of $S$ of prime order, we complete the determination of the precise value of $α_S(x)$. |
| title | Conjugate generation of sporadic almost simple groups |
| topic | Group Theory 20D08 |
| url | https://arxiv.org/abs/2505.05173 |