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arXiv · 2404.11077

Sylow theorems for supergroups

Vera Serganova·Alexander Sherman·Dmitry Vaintrob
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Abstract

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.

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BibTeXRIS

Vera Serganova, Alexander Sherman, Dmitry Vaintrob. 2024-04-17. Sylow theorems for supergroups. https://arxiv.org/abs/2404.11077

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