Refined conjugate generation in sporadic groups
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918375111786496 |
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| author | Revin, Danila O. Zavarnitsine, Andrei V. |
| author_facet | Revin, Danila O. Zavarnitsine, Andrei V. |
| contents | Given an automorphism $x$ of order bigger than $2$ of a sporadic simple group $S$, we show that there are at most $3$ conjugates of $x$ required to generate a subgroup of order divisible by a fixed prime divisor $r$ of $|S|$. The only exception is the case where $S=Suz$, $x$ is in class $3A$, $r=11$, and then the required number of generators is $4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18027 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Refined conjugate generation in sporadic groups Revin, Danila O. Zavarnitsine, Andrei V. Group Theory 20D06, 20E28, 20E45 Given an automorphism $x$ of order bigger than $2$ of a sporadic simple group $S$, we show that there are at most $3$ conjugates of $x$ required to generate a subgroup of order divisible by a fixed prime divisor $r$ of $|S|$. The only exception is the case where $S=Suz$, $x$ is in class $3A$, $r=11$, and then the required number of generators is $4$. |
| title | Refined conjugate generation in sporadic groups |
| topic | Group Theory 20D06, 20E28, 20E45 |
| url | https://arxiv.org/abs/2602.18027 |