Let H be a subgroup of finite non-abelian group G and g∈G. Z(H,G)={x∈H:xy=yx,∀y∈G}. We introduce the graph ΔH,Gg whose vertex set is G\Z(H,G) two distinct vertices x y are adjacent if x∈H or y∈H [x,y]≠g,g−1, where [x,y]=x−1y−1xy. In this paper, we determine whether tree among other results. also discuss about its diameter connectivity with special attention to dihedral groups.

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

Murali and Makamba (2001) introduced an equivalence of fuzzy subgroups. Dudek Jun (2004) studied the defined by in ideals a BCI-algebra. In this paper, we obtained sequence BCI-algebra X from ideal on X. We will show that, if two are equivalent, then them equivalent. that there is relationship between with adjoint A, where A Abelian subgroup Autµ(X).

INTRODUCTION Exposure to tobacco smoke is an extremely important risk factor determining the development of respiratory diseases, cardiovascular diseases and cancer. Passive exposure is common and often not realized by the exposed subjects. Markers of tobacco smoke exposure are nicotine metabolites, i.e. cotinine and trans-3'-hydroxycotinine. OBJECTIVES The objective of the study was to asses...

Let {p1, . . . , pn} ⊆ Rd. We think of d n. How big is the largest subset X of points such that all of the distances determined by elements of ( X 2 ) are different? We show that |X| ≥ Ω(n 1 3d−3+o(1) ). This improves on the best known result which was |X| ≥ Ω(n 1 3d−2 ). Assume that no a of the points are on the same (a− 1)-hyperplane. How big is the largest subset X of points such that all of...

If a finite group G is isomorphic to a subgroup of SO(3), then G has the D2-property. Let X be a finite complex satisfying Wall’s D2-conditions. If π1(X) = G is finite, and χ(X) ≥ 1− def(G), then X ∨ S is simple homotopy equivalent to a finite 2-complex, whose simple homotopy type depends only on G and χ(X).

then we term the elements x and y n-commutative. It is not difficult to verify that »-commutativity and (1—»)-commutativity are equivalent properties of the elements x and y, that ( — ̂ -commutativity implies ordinary commutativity, and that commuting elements are »-commutative. From any concept and property involving the fact that certain elements [or functions of elements] commute, one may der...

These two topics are closely related. Here we consider some particular groups which arise most naturally as matrix groups or quotients of them, and special properties of matrix groups which are not shared by arbitrary groups. In representation theory, we consider what we learn about a group by considering all its homomorphisms to matrix groups. This article falls roughly into two parts. In the ...

In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied.

A closed subgroup $H$ of a locally compact group $G$ is confined if the closure conjugacy class in Chabauty space does not contain trivial subgroup. We establish dynamical criterion on action totally disconnected $X$ ensuring that no relatively amenable can be confined. This property equivalent to fact its Furstenberg boundary free. Our applies Neretin groups. deduce each has two inequivalent i...