Let G be a finite group and V be a finite G–module. We present upper bounds for the cardinalities of certain subsets of Irr(GV ), such as the set of those χ ∈ Irr(GV ) such that, for a fixed v ∈ V , the restriction of χ to 〈v〉 is not a multiple of the regular character of 〈v〉. These results might be useful in attacking the non–coprime k(GV )–problem.

Let G be a finite group generated by unitary reflections in a Hermitian space V , and let ζ be a root of unity. Let E be a subspace of V , maximal with respect to the property of being a ζ-eigenspace of an element of G, and let C be the parabolic subgroup of elements fixing E pointwise. If χ is any linear character of G, we give a condition for the restriction of χ to C to be trivial in terms o...

the aim of this note is to characterize the finite groups in which all non-linear irreducible characters have distinct zero entries number.

Abstract We present a new method for showing that groups are virtually special. This is done by considering finite quotients and linear characters. use this to show an infinite family of groups, related Bestvina-Brady branching, provides examples special outside hyperbolic context.


 The Norton product is defined on each eigenspace of a distance regular graph by the orthogonal projection entry-wise product. resulting algebra, known as commutative nonassociative algebra that useful in group theory due to its interesting automorphism group. We provide formula for Hamming using linear characters. construct large subgroup automorphisms and completely describe some cases....

Various forms of the extension problem are discussed for linear codes de ned over nite rings. The extension theorem for symmetrized weight compositions over nite Frobenius rings is proved. As a consequence, an extension theorem for weight functions over certain nite commutative rings is also proved. The proofs make use of the linear independence of characters as well as the linear independence ...

Majority of character recognition algorithms such as the use of ANNs needs segmentation of the script prior to recognition. Contrast to Western scripts, Brahmi descended South Asian scripts such as Sinhala consist of modifier symbols, which make the segmentation a difficult task that needs to be addressed as a separate issue. Further, the change of shape of the basic character (by violating mod...

This is an extended version of the talk given by the first author at the conference. We report on the outcome of some experiments with the decomposition of products of (generalized) characters of some classical groups. In particular some results of the PhD-thesis of Dirk Mattig on the products of unipotent characters of general linear groups are presented and commented. In order to obtain simil...