Commuting Involutions in Finite Simple Groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911965543137280 |
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| author | Guralnick, Robert M. Robinson, Geoffrey R. |
| author_facet | Guralnick, Robert M. Robinson, Geoffrey R. |
| contents | We prove that if $G$ is a finite simple group and $x, y \in G$ are involutions, then $|x^G \cap C_G(y)| \rightarrow \infty$ as $|G| \rightarrow \infty$. This extends results of Guralnick-Robinson and Skresanov. We also prove a related result about $C_{G}(t)/O(C_G(t))$ that does not require the classification of finite simple groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16926 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Commuting Involutions in Finite Simple Groups Guralnick, Robert M. Robinson, Geoffrey R. Group Theory 20D05 We prove that if $G$ is a finite simple group and $x, y \in G$ are involutions, then $|x^G \cap C_G(y)| \rightarrow \infty$ as $|G| \rightarrow \infty$. This extends results of Guralnick-Robinson and Skresanov. We also prove a related result about $C_{G}(t)/O(C_G(t))$ that does not require the classification of finite simple groups. |
| title | Commuting Involutions in Finite Simple Groups |
| topic | Group Theory 20D05 |
| url | https://arxiv.org/abs/2407.16926 |