1. Finite group schemes of p-rank ≤ 1
- Author
-
Rolf Farnsteiner and Hao Chang
- Subjects
Finite group ,Modular representation theory ,Pure mathematics ,Rank (linear algebra) ,Group (mathematics) ,General Mathematics ,Scheme (mathematics) ,Lie algebra ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Algebraically closed field ,Type (model theory) ,Mathematics - Abstract
Let be a finite group scheme over an algebraically closed field k of characteristic char(k) = p ≥ 3. In generalisation of the familiar notion from the modular representation theory of finite groups, we define the p-rank rkp() of and determine the structure of those group schemes of p-rank 1, whose linearly reductive radical is trivial. The most difficult case concerns infinitesimal groups of height 1, which correspond to restricted Lie algebras. Our results show that group schemes of p-rank ≤ 1 are closely related to those being of finite or domestic representation type.
- Published
- 2017