in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.

THEOREM 2. If G is a finite monolithic group with monolith M (in other words, if G is a finite group with a unique minimal normal subgroup M), then Mis a verbal subgroup ofG. These generalize the corresponding results for finite ^-groups established by Weichsel ((4), Theorems 2-1, 2-3). The second answers affirmatively a (privately communicated) question of Sheila Oates. In order to give our de...

Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...

abstract. in this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

The minimal faithful permutation degree n(G) of a finite group G is the least positive integer n such that G is isomorphic to a subgroup of the symmetric group Sn. Let AT be a normal subgroup of a finite group G. We prove that n(G/N) $C /i(G) if G/N has no nontrivial Abelian normal subgroup. There is an as yet unproved conjecture that the same conclusion holds if G/N is Abelian. We investigate ...

Skew morphisms, which generalise automorphisms for groups, provide a fundamental tool the study of regular Cayley maps and, more generally, finite groups with complementary factorisation $G=BY$, where $Y$ is cyclic and core-free in $G$. In this paper, we classify all examples $B$ monolithic (meaning that it has unique minimal normal subgroup, subgroup not abelian) As consequence, obtain classif...

‎in this paper we give a new condition for a sylow $p$-subgroup of a finite group to control transfer‎. ‎then it is deduced a characteri-zation of supersoluble groups that can be seen as a generalization of the well known result concerning the supersolubility of finite groups with cyclic sylow subgroups‎. moreover a condition for a normal embedding of a strongly closed $p$-subgroup is given‎. ...

‎for a finite group $g$ let $nu(g)$ denote the number of conjugacy classes of non-normal subgroups of $g$‎. ‎the aim of this paper is to classify all the non-nilpotent groups with $nu(g)=3$‎.

Abstract A group G is said to be an FC -group if every conjugacy class of has finite order and a T subnormal subgroup normal in . In this paper we give characterization groups that are both -groups go further the study with few non-normal subgroups sense chain conditions. The structure satisfying maximal, minimal double condition on will described.