Mixability of finite groups
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917906054381568 |
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| author | Amir, Gideon Blachar, Guy Ghosh, Subhajit Vishne, Uzi |
| author_facet | Amir, Gideon Blachar, Guy Ghosh, Subhajit Vishne, Uzi |
| contents | Say that a finite group $G$ is mixable if a product of random elements, each chosen independently from two options, can distribute uniformly on $G$. We present conditions and obstructions to mixability. We show that $2$-groups, the symmetric groups, the simple alternating groups, several matrix and sporadic simple groups, and most finite Coxeter groups, are mixable. We also provide bounds on the mixing length of such groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17806 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixability of finite groups Amir, Gideon Blachar, Guy Ghosh, Subhajit Vishne, Uzi Group Theory Probability Representation Theory Say that a finite group $G$ is mixable if a product of random elements, each chosen independently from two options, can distribute uniformly on $G$. We present conditions and obstructions to mixability. We show that $2$-groups, the symmetric groups, the simple alternating groups, several matrix and sporadic simple groups, and most finite Coxeter groups, are mixable. We also provide bounds on the mixing length of such groups. |
| title | Mixability of finite groups |
| topic | Group Theory Probability Representation Theory |
| url | https://arxiv.org/abs/2501.17806 |