Title of article :
The Probability that an Element of Metacyclic 2-Groups of Positive Type Fixes a Set
Author/Authors :
El-sanfaz, Mustafa Anis Universiti Teknologi Malaysia - Faculty of Science - Department of Mathematical Sciences, Malaysia , Sarmin, Nor Haniza Universiti Teknologi Malaysia - Faculty of Science - Department of Mathematical Sciences, Malaysia , Omer, Sanaa Mohamed Saleh University of Benghazi - Faculty of Science - Department of Mathematics, Libya
Abstract :
In this paper, G is a metacyclic 2-group of positive type of nilpotency of class at least three. Let Ω be the set of all subsets of all commuting elements of G of size two in the form of (a,b), where a and b commute and each of order two. The probability that an element of a group fixes a set is considered as one of the extensions of the commutativity degree that can be obtained by some group actions on a set. In this paper, we compute the probability that an element of G fixes a set in which G acts on a set, Ω by conjugation.
Keywords :
Commutativity degree , metacyclic groups , group action
Journal title :
Jurnal Teknologi :F
Journal title :
Jurnal Teknologi :F
