On minimal subdegrees of finite primitive permutation groups

QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...

Groups with Two Extreme Character Degrees and their Minimal Faithful Representations

for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...

Intersection Matrices for Finite Permutation Groups*

In this paper we study finite transitive groups G acting on a set Q. The results, which are trivial for multiply-transitive groups, directly generalize parts of the discussion of rank-3 groups in [4] and [5l. There arc close connections with Feit and Higman’s paper [2]. For each a EQ let us choose a G,-orbit d(a) # {CZ} so that d(a)8 = d(a”) for all a E Sz and g E G. Relative to LI we introduce...

Characterization of Families of Rank 3 Permutation Groups by the Subdegrees I

On minimal degrees of faithful quasi-permutation representations of nilpotent groups

By a quasi-permutation matrix, we mean a square non-singular matrix over the complex field with non-negative integral trace....