On permutation representations of polyhedral 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...

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 fai...

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....

Finding Minimal Permutation Representations of Finite Groups

A minimal permutation representation of a finite group G is a faithful G-set with the smallest possible cardinality. We study the structure of such representations and show that for most groups they may be obtained by a greedy construction. It follows that whenever the algorithm works (except when central involutions intervene) all minimal permutation representations have the same set of orbit ...

Decomposing permutation representations of symmetric groups