Abstract A finite group G G is called an MSN-group if all maximal subgroups of the Sylow are subnormal in . In this article, we investigate structure groups such that a non-MSN-group even order which every subgroup MSN-group. addition, determine minimal simple whose second MSN-groups.

We study 3-dimensional Poincaré duality pro-p groups in the spirit of work by Robert Bieri and Jonathan Hillmann, show that if such a group G has nontrivial finitely presented subnormal subgroup infinite index, then either is cyclic normal or polycyclic Demushkin an open G. Also, we describe centralizers generated subgroups groups.

A subgroup H is said to be weakly c∗-normal in a group G if there exists a subnormal subgroup K of G such that HK = G and H ∩ K is s-quasinormally embedded in G. We give some results which generalize some authors’ results.

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.

The generalised Fitting subgroup of a finite group is the group generated by all subnormal subgroups that are either nilpotent or quasisimple. The importance of this subgroup in finite group theory stems from the fact that it always contains its own centraliser, so that any finite group is an abelian extension of a group of automorphisms of its generalised Fitting subgroup. We define a class of...

Let $G$ be a permutation group on set $\Omega$. A base for is subset of $\Omega$ whose pointwise stabiliser trivial, and the size minimal cardinality base. If has $2$, then corresponding Saxl graph $\Sigma(G)$ vertex two vertices are adjacent if they form $G$. recent conjecture Burness Giudici states that finite primitive with property every have common neighbour. We investigate this when an af...

Let $$D$$ be a division ring and $$K$$ subfield of which is not necessarily contained in the center $$F$$ . We study structure under condition left algebraicity certain subsets over Among others, it proved that if $$D^*$$ contains noncentral normal subgroup algebraic bounded degree $$d$$ , then $$[D:F]\le d^2$$ In case $$K=F$$ obtained results show either all additive commutators or multiplicat...

This paper aims at studying solvable-by-finite and locally solvable maximal subgroups of an almost subnormal subgroup the general skew linear group $\GL_n(D)$ over a division ring $D$. It turns out that in case where $D$ is non-commutative, if such exist, then either it abelian or $[D:F]<\infty$. Also, $F$ infinite field $n\geq 5$, every normal $\GL_n(F)$ abelian.

Let V be a finite-dimensional vector space over finite field, and suppose G??L(V) is group with unique subnormal quasisimple subgroup E(G) that absolutely irreducible on V. A base for G set of vectors B?V pointwise stabiliser GB=1. If has size 1, we say it regular orbit In this paper investigate the minimal groups E(G)/Z(E(G))?PSLn(q) in defining characteristic, an aim classifying those