Primitivity of Permutation Groups, Coherent Algebras and Matrices

Algebraic Combinatorics in Mathematical Chemistry. Methods and Algorithms. I. Permutation Groups and Coherent (cellular) Algebras

Let (G;) be a permutation group of degree n. Let V (G;) be the set of all square matrices of order n which commute with all permutation matrices corresponding to permutations from (G;): V (G;) is a matrix algebra which is called the centralizer algebra of (G;): In this paper we introduce the combinatorial analogue of centralizer algebras, namely coherent (cellular) algebras and consider the pro...

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...

A study of permutation groups and coherent configurations

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii CHAPTER 1. HISTORICAL BACKGROUND . . . . . . . . . . . . . . . . . 1 1.1 Early Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Resolvent Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 More Recent Developments . . . . . . . . . . . . . . . . . ....

I . Permutation Groups and Coherent ( Cellular ) Algebras

Finitary Permutation Groups

A finitary permutation group is a natural generalization of a finite permutation group. The structure of a transitive finitary permutation group is surprisingly simple when its degree is infinite. Here we study primitivity, following P. M. Neumann’s work in the 1970s. We also study generalized solubility conditions on these groups. These notes arose from lectures aimed at an audience who had se...