### A computational verification of Alperin's weight conjecture for groups of small order and their prime fields.

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We introduce in this article a new method to calculate all absolute and relatif primitive invariants of finite groups. This method is inspired from K. Girstmair which calculate an absolute primitive invariant of minimal degree. Are presented two algorithms, the first one enable us to calculate all primitive invariants of minimal degree, and the second one calculate all absolute or relative primitive invariants with distincts coefficients. This work take place in Galois Theory and Invariant Theory. ...

MSC 2010: 33C15, 33C05, 33C45, 65R10, 20C40The paper contains some new formulas involving the Whittaker functions and arising as the values of some double integrals, which are invariant with respect to the representation of the group SO(2; 1).

This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra $\mathbb{F}{S}_{n}$ of the symmetric group ${S}_{n}$ over a field $\mathbb{F}$ of characteristic 0 (or $p>n$). The goal is to obtain a constructive version of the isomorphism $\psi :{\u2a01}_{\lambda}{M}_{{d}_{\lambda}}\left(\mathbb{F}\right)\u27f6\mathbb{F}{S}_{n}$ where $\lambda $ is a partition of $n$ and ${d}_{\lambda}$ counts the standard tableaux of shape $\lambda $....

In this paper we calculate the 3-modular character table of the twisted Chevalley group 2D4(2) and its automorphism group 2D4(2).2. The Meat-Axe package for calculating modular characters over finite fields (Ryba (1990)) was used to calculate most of the characters. The method of condensation, which was explained in Suleiman (1990) was used to determine the complete character table. All these methods are explained later in this paper.