Sylow theorems for supergroups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916210162008064 |
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| author | Serganova, Vera Sherman, Alexander Vaintrob, Dmitry |
| author_facet | Serganova, Vera Sherman, Alexander Vaintrob, Dmitry |
| contents | We introduce Sylow subgroups and $0$-groups to the theory of complex algebraic supergroups, which mimic Sylow subgroups and $p$-groups in the theory of finite groups. We prove that Sylow subgroups are always $0$-groups, and show that they are unique up to conjugacy. Further, we give an explicit classification of $0$-groups which will be very useful for future applications. Finally, we prove an analogue of Sylow's third theorem on the number of Sylow subgroups of a supergroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11077 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sylow theorems for supergroups Serganova, Vera Sherman, Alexander Vaintrob, Dmitry Representation Theory Mathematical Physics Group Theory We introduce Sylow subgroups and $0$-groups to the theory of complex algebraic supergroups, which mimic Sylow subgroups and $p$-groups in the theory of finite groups. We prove that Sylow subgroups are always $0$-groups, and show that they are unique up to conjugacy. Further, we give an explicit classification of $0$-groups which will be very useful for future applications. Finally, we prove an analogue of Sylow's third theorem on the number of Sylow subgroups of a supergroup. |
| title | Sylow theorems for supergroups |
| topic | Representation Theory Mathematical Physics Group Theory |
| url | https://arxiv.org/abs/2404.11077 |