On co-cyclic probability for a generalized quaternion

Abstract

 The co-cyclic probability for a finite group  is introduced in this paper; the quantity measures the probability of randomly selecting a pair of elements  such that the pair belongs to a cyclic subgroup of the group under consideration. The group considered is the generalized quaternion , a pattern for computing the probability is obtained via permutation approach and it is shown that it lies in the interval  . Illustrations where done for some n.