‎Let $G$ be a finite group and $nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$‎. ‎In this paper‎, ‎all nilpotent groups $G$ with $nu(G)=3$ are classified‎.  

Introduction. Let G be a Lie group and M a compact C manifold. In [2] Anosov actions of G on M are defined and proved to be structurally stable. In this announcement we are concerned with the foliation ^ of M defined by the orbits of G. Under the assumption that G is connected, # is C stable (3). If G is connected and nilpotent, G has a compact orbit (4). If G is merely solvable, however, there...

The aim of this paper is to prove Theorem 1.1 below, a generalization to virtually nilpotent spaces of a result of Wilkerson [13] and Sullivan [12]. We recall that a CW complex Y is virtually nilpotent if (i) Y is connected, (ii) 7r~ Y is virtually nilpotent (i.e. has a nilpotent subgroup of finite index) and (iii) for every integer n > 1, zr~Y has a subgroup of finite index which acts nilpoten...

We show that the outer automorphism groups of graph products finitely generated abelian satisfy Tits alternative, are residually finite, their so-called Torelli subgroups generated, and they a dichotomy between being virtually nilpotent containing non-abelian free subgroup is determined by graphical condition on underlying labelled graph. Graph simultaneously generalize right-angled Artin (RAAG...

A perfect code in a graph ?=(V,E) is subset C of V such that no two vertices are adjacent and every vertex V?C to exactly one C. subgroup H group G called if there exists Cayley which admits as code. Equivalently, an inverse-closed containing the identity element (A,H) tiling sense can be uniquely expressed product H. In this paper we obtain multiple results on codes finite groups, including fe...

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 ...

In this paper, we deal with Molaei’s generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of ...

In this paper, we give some new characterizations of finite p-nilpotent groups by using the notion of HC-subgroups and extend several recent results. Mathematics Subject Classification (2010). 20D10, 20D20.

We investigate the minimum distance of the error correcting code formed by the homomorphisms between two finite groups G and H. We prove some general structural results on how the distance behaves with respect to natural group operations, such as passing to subgroups and quotients, and taking products. Our main result is a general formula for the distance when G is solvable or H is nilpotent, i...