Tootfinder

Sylow theorems for supergroups
Vera Serganova, Alexander Sherman, Dmitry Vaintrob
https://arxiv.org/abs/2404.11077 https://arxiv.org/…

Sylow theorems for supergroups
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.