Regular orbits on symplectic modules
Let G be a group of odd order and let V be a faithful and completely reducible KG-module, char(K)\(\neq 2\). Assume that V is endowed with a non- singular symplectic form fixed by G. Then V contains a regular G-orbit, i.e. there exists \(v\in V\) such that \(C_ G(v)=1\). The result is false when \(| G|\) is even or \(char(K)=2\). Using this result, a very strong theorem of Hall-Higman type for groups of odd order is obtained.
scientific article; zbMATH DE number 4067172