Counting Centralizers of a Finite Group with an Application in Constructing the Commuting Conjugacy Class Graph
نویسندگان
چکیده
The set of all centralizers elements in a finite group G is denoted by Cent(G) and called n-centralizer if |Cent(G)|=n. In this paper, the structure non-abelian with property that GZ(G)≅Zp2⋊Zp2 obtained. As consequence, it proved such has exactly [(p+1)2+1] element commuting conjugacy class graph completely determined.
منابع مشابه
A NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS
The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.
متن کاملThe Automorphism Group of Commuting Graph of a Finite Group
Let G be a finite group and X be a union of conjugacy classes of G. Define C(G,X) to be the graph with vertex set X and x, y ∈ X (x 6= y) joined by an edge whenever they commute. In the case that X = G, this graph is named commuting graph of G, denoted by ∆(G). The aim of this paper is to study the automorphism group of the commuting graph. It is proved that Aut(∆(G)) is abelian if and only if ...
متن کاملA Kind of Non-commuting Graph of Finite Groups
Let g be a fixed element of a finite group G. We introduce the g-noncommuting graph of G whose vertex set is whole elements of the group G and two vertices x,y are adjacent whenever [x,y] g and [y,x] g. We denote this graph by . In this paper, we present some graph theoretical properties of g-noncommuting graph. Specially, we investigate about its planarity and regularity, its clique number a...
متن کاملan investigation of the types of text reduction in subtitling: a case study of the persian film gilaneh with english subtitles
چکیده ندارد.
15 صفحه اولRemarks On Commuting Graph of a Finite Group
The commuting graph ∆(G) of a group G is the graph whose vertex set is the group and two distinct elements x and y being adjacent if and only if xy = yx. In this paper the automorphism group of this graph is investigated. We observe that Aut(∆(G)) is a non-abelian group such that its order is not prime power and square-free.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2022
ISSN: ['1532-4125', '0092-7872']
DOI: https://doi.org/10.1080/00927872.2022.2125982