Hall-Higman type theorems. V

Thomas Berger
1977 Pacific Journal of Mathematics  
This paper sets out the inductive machinery which makes the computations of other numbers of this sequence useful. Representation theory is cast in the framework of wreath products which are then used to study the behavior of regular orbits and modules under various types of induction. Tensor induction is defined and studied along with the related concept of form primitivity. Let AG be a solvable group with normal subgroup G and nilpotent complement A where (\A\, \G\) = 1. Assume that A: is a
more » ... eld and that V is a faithful irreducible k [AG]-module. This series considers the following two questions. = -9(u 2 , ωv,) . HALL-HIGMAN TYPE THEOREMS V 5 V\ N == V 1 + * 4-V t where the F* are homogeneous components. If H is the stabilizer in G of V 1 then restriction to V x is an isomorphism of Ή.orύ kίG i(V) V) onto Hom^j^Fi, VΊ).
doi:10.2140/pjm.1977.73.1 fatcat:4tqzltekszeijo2yet2femad3e