‎In 1970‎, ‎Menegazzo [Gruppi nei quali ogni sottogruppo e intersezione di sottogruppi massimali‎, ‎ Atti Accad‎. ‎Naz‎. ‎Lincei Rend‎. ‎Cl‎. ‎Sci‎. ‎Fis‎. ‎Mat‎. ‎Natur. 48 (1970)‎, ‎559--562.] gave a complete description of the structure of soluble $IM$-groups‎, ‎i.e.‎, ‎groups in which every subgroup can be obtained as intersection of maximal subgroups‎. ‎A group $G$ is said to have the $FM$...

in this paper we present some results about subgroup which is generalization of the subgroup $r_{2}^{otimes}(g)={ain g|[a,g]otimes g=1_{otimes},forall gin g}$ of right $2_{otimes}$-engel elements of a given group $g$. if $p$ is an odd prime, then with the help of these results, we obtain the results about tensor squares of p-groups satisfying the law $[x,g,y]otimes g=1_{otimes}$, for all $x, g,...

Let G2(q) be the finite Chevalley group of type G2 defined over a finite field with q = p elements, where p is a prime number and n is a positive integer. In this paper, we determine when the restriction of an absolutely irreducible representation of G in characteristics other than p to a maximal subgroup of G2(q) is still irreducible. Similar results are obtained for B2(q) and G2(q).

In this paper, we give a simple method for computing the stabilizer subgroup of D(f) = {α ∈ Fq | there is a β ∈ Fq such that βn = f(α)} in PSL2(Fq), where q is a large odd prime power, n is a positive integer dividing q − 1 greater than 1, and f(x) ∈ Fq[x]. As an application, we construct new infinite families of 3-designs.

In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups Zn⋊Zq. The definition of the semi-direct product depending on the choice of an homomorphism, we first analyze the different possibilities for this homomorphism in function of n and q. Then, we present a polynomial-time quantum algorithm for the case Zpr ⋊ Zp when p is an odd prime.

Let q be a power of a prime p. Let P be a parabolic subgroup of the general linear group GLn(q) that is the stabilizer of a flag in F n q of length at most 5, and let U = Op(P ). In this note we prove that, as a function of q, the number k(U) of conjugacy classes of U is a polynomial in q with integer coefficients.

Let G ⊂ SL(n, C) be a finite subgroup and φ:Y → X = C/G any resolution of singularities of the quotient space. We prove that crepant exceptional prime divisors of Y correspond one-to-one with “junior” conjugacy classes of G. When n = 2 this is a version of the McKay correspondence (with irreducible representations of G replaced by conjugacy classes). In the case n = 3, a resolution with KY = 0 ...