Hall Higman type theorems II

HALL-HIGMAN TYPE THEOREMS -II (M.Sc. Thesis) İhrahim GÜNALTILI GAZt. UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOLOGY September 1990 ABSTRACT In this work, we studied the paper of T.R. Berger entitled "Hall-Higman type theorems, II" [ 1] In this paper, we obtain a complete classification of all minimal modules over K = GF(r) for nilpotent groups (r > 1 a prime). Suppose K =¦ GF(r). is a field for a prime r;uH is nilpotent; V is a faithful irreducible K[ H] -module; g is a non-singuler symplectic bilinear form upon V and H fixes the form g. In this case, the structure of H is determined completely. It's representation upon V is described when V is symplectic primitive K [H] -mo dule. In this thesis, we have prepared a detailed and readable account of the above mentioned works of Berger; we have clarified many points and filled in many gaps. T.R. Berger had shown before that one of the condition in the definition of a minimal module was unnecessary we have also shown this in elementary way. 1X1