Sylow theorems for supergroups
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.
 Publication:

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.11077
 arXiv:
 arXiv:2404.11077
 Bibcode:
 2024arXiv240411077S
 Keywords:

 Mathematics  Representation Theory;
 Mathematical Physics;
 Mathematics  Group Theory
 EPrint:
 33 pages