The Probability That an Element of the Dihedral Groups Fixes a Set

摘要

In this paper, let G be a dihedral group of order 2n. Let Ω be the set of all subsets of commuting elements of size two in the form of (a, b), where a and b commute and |a| = |b| = 2. The probability that an element of a group fixes a set is considered as one of the generalizations of the commutativity degree that can be obtained by some group actions on a set. In this paper, the probability that an element of G fixes the set Ω is computed.