the non-split extension group $overline{g} = 5^3{^.}l(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in ly. the group $overline{g}$ in turn has l(3,5) and $5^2{:}2.a_5$ as inertia factors. the group $5^2{:}2.a_5$ is of order 3 000 and is of index 124 in l(3,5). the aim of this paper is to compute the fischer-clifford matrices of $overline{g}$, which together with associated parti...

It is well known that there a positive relationship between the maximal multiplicity and length of associated virtual 1-parameter subgroup projective hypersurface. In this article, we will define classes hypersurfaces construct them from Hesselink stratification Hilbert scheme.

Let G be a connected semisimple Lie group such that the associated symmetric space X is Hermitian and let Γg be the fundamental group of a compact orientable surface of genus g ≥ 2. We survey the study of maximal representations of Γg into G that is the subset of Hom(Γg, G) which is a union of components characterized by the maximality of the Toledo invariant ([16] and [14]). Then we concentrat...

Let G be a finite p-group, M is a subgroup of G. M is called fullnormal if for any subgroup K of M, we have K G. In this paper, We determine the structure of finite p-groups which have a maximal subgroup is full-normal(p > 2). Mathematics Subject Classification: 20D10, 20D15

In this paper we describe the relationship between finite free resolutions of perfect ideals in split format (for Dynkin formats) and certain intersections opposite Schubert varieties with big cell for homogeneous spaces $G/P$ where $P$ is a maximal parabolic subgroup.

What ingredients are necessary to describe all maximal subgroups of the general finite group G? This paper is concerned with providing such an analysis. A good first reduction is to take into account the first isomorphism theorem, which tells us that the maximal subgroups containing a given normal subgroup N of G correspond, under the natural projection, to the maximal subgroups of the quotient...

The study of the free idempotent generated semigroup IG(E) over a biordered set E began with the seminal work of Nambooripad in the 1970s and has seen a recent revival with a number of new approaches, both geometric and combinatorial. Here we study IG(E) in the case E is the biordered set of a wreath product G ≀ Tn, where G is a group and Tn is the full transformation monoid on n elements. This...

In the first part of these notes we shall try to describe the main ideas in the theory. Let G be a reductive algebraic matrix group over Q. Then G(A) is the restricted direct product over all valuations v of the groups G(Qu). If v is finite, define Ku to be G(uJ if this latter group is a special maximal compact subgroup of G(Qu). This takes care of almost all v. For the remaining finite v, we l...

in this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $l$-setting. this construction is illustrated by an example. we also prove that for an $l$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $l$-subset provided the given $l$-subset possesses sup-property.