‎Let $f:Arightarrow B$ and $g:A rightarrow C$ be two ring homomorphisms and let $J$ and $J^{'}$ be two ideals of $B$ and $C$‎, ‎respectively‎, ‎such that $f^{-1}(J)=g^{-1}(J^{'})$‎. ‎The bi-amalgamation of $A$ with $(B,C)$ along $(J,J^{'})$ with respect of $(f,g)$ is the subring of $Btimes C$ given by‎ ‎$Abowtie^{f,g}(J,J^{'})={(f(a)+j,g(a)+j^{'})‎/ ‎a in A‎, ‎(j,j^{'}) in Jtimes J^{'}}.$‎ ‎In ...

G. Navarro raised the question whether the ordinary character table X(G) of a finite group G determines the Sylow numbers of G. In this note we show that this is the case when G is nilpotent-by-nilpotent, quasinilpotent, Frobenius group or a 2-Frobenius group. In particular Sylow numbers of supersoluble groups are determined by their ordinary character table. If G and H are finite groups with i...

In this project, we are going to study some results concerning the character rings and Heche Algebras in Sk and GL(k, F ). In next section, we will introduce some notation system in Sk and GL(k, F ) first, and with that, we will deduce some interesting and important results in this field, such as the results about the length function on W and the double B − B cosets, where W is the Weyl group o...

in a previous paper, the second author established that, given finite fields $f < e$ and certain subgroups $c leq e^times$, there is a galois connection between the intermediate field lattice ${l mid f leq l leq e}$ and $c$'s subgroup lattice. based on the galois connection, the paper then calculated the irreducible, complex character degrees of the semi-direct product $c rtimes {rm gal} (e/f)$...

The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational character tables are also considered into account.The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational charact...