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.