On the commuting probability and supersolvability of finite groups
نویسندگان
چکیده
منابع مشابه
On the Commuting Probability in Finite Groups
Introduction: When G is a finite group, we may endow G×G with the structure of a probability space by assigning the uniform distribution. As was pointed out by W.H. Gustafson [10], the probability that a randomly chosen pair of elements of G commute is then k(G) |G| , where k(G) is the number of conjugacy classes of G. We denote this probability by cp(G). It was also noted in [10] that cp(G) ≤ ...
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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...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2013
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-013-0535-9