We construct self-orthogonal codes from the row span over F2 or F3 of the adjacency matrices of some strongly regular graphs defined by the rank-3 action of the simple unitary group U4(3) on the conjugacy classes of some of its maximal subgroups. We establish some properties of these codes and the nature of some classes of codewords.

By constructing, in the relative case, objects analoguous to Rips and Sela’s canonical representatives, we prove that the set of conjugacy classes of images by morphisms without accidental parabolic, of a finitely presented group in a relatively hyperbolic group, is finite. An important result of W.Thurston is : Theorem 0.1 ([T] 8.8.6) Let S be any hyperbolic surface of finite area, and N any g...

0. Introduction 1105 1. Constructible families 1111 2. Genericity for finite subgroups 1116 3. Finite groups of Lie type 1119 4. Basic nonconcentration estimate 1122 5. Finite subgroups of abelian varieties 1126 6. Orders of conjugacy classes and centralizers 1127 7. Regular semisimple and unipotent elements 1129 8. Minimal unipotent elements 1134 9. Frobenius map 1140 10. Traces in the basic c...

Let G be a finite group and S proper subgroup of G. A is called an S-(CAP)-group if every local either CAP-subgroup or conjugate to
 S. The main purpose this construction to demonstrate new way analyzing the structure by properties number conjugacy classes its subgroups.

Let $G$ be a non-abelian group. The non-commuting graph $Gamma_G$ of $G$ is defined as the graph whose vertex set is the non-central elements of $G$ and two vertices are joined if and only if they do not commute.In this paper we study some properties of $Gamma_G$ and introduce $n$-regular $AC$-groups. Also we then obtain a formula for Szeged index of $Gamma_G$ in terms of $n$, $|Z(G)|$ and $|G|...

Many non-Abelian finite subgroups of SU(3) have been used to explain the flavor structure of the Standard Model. In order to systematize and classify successful models, a detailed knowledge of their mathematical structure is necessary. In this paper we shall therefore look closely at the series of finite non-Abelian groups known as ∆(6n), its smallest members being S3 (n = 1) and S4 (n = 2). Fo...