Suppose that V = V10 Vz 0. 0 Vt where the Vt are k ...... Let JS; be the stabilizer in K of g. Since [L, Îf] = 1 and (|L|, |Îf |) = 1 we have Kg. = Lg x Îf^. For yf* e Kg, ...
PACIFIC JOURNAL OF MATHEMATICS Vol. 73, No. 1, 1977
HALL-HIGMAN TYPE THEOREMS V T. R.
BERGER
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 field and that V is a faithful irreducible k [AG]-module. This series considers the following two questions. (1) If k ~ GF(r) for a prime r, then when (Joes the permutation representation of A on F # contain a regular orbit? (2) If i?
