The purpose of this note is to determine all endotrivial modules in prime characteristic p, for a finite group having a cyclic Sylow p-subgroup. In other words, we describe completely the group of endotrivial modules in that case. The endotrivial modules are a family of finitely generated modules for a group algebra of a finite group which appear naturally in modular representation theory. Seve...

In 1] M. Aschbacher described the structure of the possible maximal subgroups of a classical group G with natural module M. Each such subgroup is either a member of a canonical class of subgroups, or it is the normalizer of a quasi-simple, absolutely irreducible subgroup H of G. In the latter case suppose that H is a classical group whose deening characteristic is coprime to that of G. The aim ...

The present paper is devoted to studying the maps corresponding suborbital graphs for normalizer ΓB(N) of Γ0(N) modulo N, where N denotes a positive integer. We reveal complete structure these maps, finding their vertices, edges, darts, and faces explicitly. we investigated in were all regular large genus except some low values N.

Quantification of gene expression is important to confirm changes in levels of gene expression in disease. Prior quantification methods include standard curves, absolute quantification, and relative quantification. This paper describes an analytic method for the relative quantification of Presenilin-1 (PS-1) in neurons and Forkhead-box (FOX) p3 in PBMNCs using real-time PCR analytic techniques....

We investigate the class of N -determined p-compact groups and the class of p-compact groups with N -determined automorphisms. A p-compact group is said to be N -determined if it is determined up to isomorphism by the normalizer of a maximal torus. The automorphisms of a p-compact group are said to be N -determined if they are determined by their restrictions to this maximal torus normalizer.

Malware is code designed for a malicious purpose, such as obtaining root privilege on a host. A malware detector identifies malware and thus prevents it from adversely affecting a host. In order to evade detection by malware detectors, malware writers use various obfuscation techniques to transform their malware. There is strong evidence that commercial malware detectors are susceptible to thes...

Let Fn q be a vector space of dimension n over the finite field Fq . A q-analog of a Steiner system (also known as a q-Steiner system), denoted Sq(t,k,n), is a set S of k-dimensional subspaces of Fn q such that each t-dimensional subspace of Fn q is contained in exactly one element of S . Presently, q-Steiner systems are known only for t = 1, and in the trivial cases t = k and k= n. In this pap...

Let X be a smooth projective connected curve of genus g ≥ 2 defined over an algebraically closed field k of characteristic p > 0. Let G be a finite group, P a Sylow p-subgroup of G and NG(P ) its normalizer in G. We show that if there exists an étale Galois cover Y → X with group NG(P ), then G is the Galois group wan étale Galois cover Y → X , where the genus of X depends on the order of G, th...

Let Xns(11) denote the modular curve associated to the normalizer of a non-split Cartan subgroup of level 11; see [10, Appendix]. This curve has genus 1, is defined over Q and parametrizes elliptic curves with a certain level 11 structure. The interest of Theorem 1.1 lies in the fact that Xns(11) is isomorphic over Q to the curve E and that rational points (x, y) on E for which x/(xy − 11) is i...