The Co-Prime Probability of p-Groups

  • Norarida Abd Rhani Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Cawangan Kelantan
  • Nor Muhainiah Mohd Ali Department of Mathematical Sciences, Faculty of Science,Universiti Teknologi Malaysia
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia
  • Ahmad Erfanian Department of Pure Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Keywords: Commutativity degree, Co-prime probability, Finite group, p-Groups


The commutativity degree of G can be used to measure how close a group is to be abelian.This concept has been extended to the probability that two random integers are co-prime. Two integers s and t are said to be co-prime if their greatest common divisor is equal to one. This concept has been
further extended to the co-prime probability of G, where the probability of the order of a random pair of elements in the group are co-prime. In this paper, the co-prime probability for all p-groups, where p is prime number is determined.