# The Co-Prime Probability of p-Groups

Keywords:
Commutativity degree, Co-prime probability, Finite group, p-Groups

### Abstract

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.

Published

2019-06-10

Section

Articles