Suppose | G | = n and m ∈ N is such that gcd(m, n) = 1. If g ∈ G and g^m = e,prove that g = e
Question
Solution 1
To prove that g = e, we need to use the fact that the order of an element divides the order of the group.
Step 1: Let's denote the order of g as k. This means that g^k = e and k is the smallest such positive integer.
Step 2: Since g^m = e, the order of g, k, must divide m (because m is the power Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI
Similar Questions
Suppose | G | = n and m ∈ N is such that gcd(m, n) = 1. If g ∈ G and g^m = e,prove that g = e
Prove the equality gcd(m, n) = gcd(n, m mod n) for every pair of positiveintegers m and n
Suppose there are integers 𝑎𝑎, 𝑏𝑏, 𝑥𝑥 and 𝑦𝑦 such that 𝑎𝑥+𝑏𝑦=5𝑎𝑥+𝑏𝑦=5, and 55 does not divide 𝑥𝑥. What is gcd(𝑥,𝑦)gcd(𝑥,𝑦)?
prove that {1/n} n=1 to inf is not compact in R with usual metric. suppose use the adjoint point {0} to {1/n} n=1 to inf
Suppose that events M and N are two mutually exclusive events, with P(M) = 0.4 and P (N) = 0.5 . Calculate P ( N' | M') ?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.