We present a method of bounding incomplete character sums for finite abelian groups with arguments produced by a first-order recursion. This method is particularly effective if the recursion involves a special type of permutation called an R-orthomorphism. Examples of Rorthomorphisms are given.

We introduce a database containing the character tables of the endomorphism rings of the multiplicity-free permutation modules of the sporadic simple groups, their automorphism groups, their Schur covers, and their bicyclic extensions. We describe the techniques used to compile the data, and present a couple of applications to orbital graphs. MSC: 20C34, 20C40, 20B25, 20B40, 20D08, 05C25.

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...

a special class of cubic graphs are the cycle permutation graphs. a cycle permutation graph pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.in this paper we determine a good upper bound for tenacity of cycle permutation graphs.

A permutation with no fixed points is called a derangement.The subset $mathcal{D}$ of a permutation group is derangement if all elements of $mathcal{D}$ are derangement.Let $G$ be a permutation group, a derangementgraph is one with vertex set $G$ and derangement set $mathcal{D}$ as connecting set. In this paper, we determine the spectrum of derangement graphs of order a product of three primes.

In this paper, our main objective is to combinatorially obtain all characteristic class functions of the Weyl group type G2 with help structure generalized descent algebra including Solomon’s and Mantaci-Reutenauer algebra. We also give an interpretation character table in terms permutation characters defined on set cosets belonging each its some special subgroups.

In this paper, by using the notion of fuzzy subsets, the concept of F-permutation is introduced. Then by applying this notion the concepts of presentation of an F-polygroup, graph of an F-permutation and F-permutation matrices are investigated.

We determine the character table of the endomorphism ring of the permutation module associated with the multiplicity-free action of the sporadic simple Baby Monster group B on its conjugacy class 2B, where the centraliser of a 2B-element is a maximal subgroup of shape 2.Co2. This is one of the first applications of a new general computational technique to enumerate big orbits. Mathematics Subje...

Suppose that G is a …nite solvable group which has an irreducible character which vanishes on exactly one conjugacy class. Then we show that G has a homomorphic image which is a nontrivial 2-transitive permutation group. The latter groups have been classi…ed by Huppert. We can also say more about the structure of G depending on whether is primitive or not. Mathematics Subject Classi…cation 2000...

Cameron, P.J. and A.M. Cohen, On the number of fixed point free elements in a permutation group, Discrete Mathematics 106/107 (1992) 135138. A lower bound is given for the number of fixed point free elements in a permutation group. At the end of May, 1991, H.W. Lens&a Jr asked the second author whether the number of fixed point free elements of a finite transitive group on a set of n elements, ...