Solution Found!
Provethatife: G -+ His a homomorphism, a E G, and o(a) is finite, theno(e(a!o(a)
Chapter 21, Problem 21.17(choose chapter or problem)
QUESTION:
Prove that if \(\theta: G \rightarrow H\) is a homomorphism, \(a \in G\), and o(a) is finite, then \(o(\theta(a)) \mid o(a)\).
Questions & Answers
QUESTION:
Prove that if \(\theta: G \rightarrow H\) is a homomorphism, \(a \in G\), and o(a) is finite, then \(o(\theta(a)) \mid o(a)\).
ANSWER:Step 1 of 4
Given \(\theta: G \rightarrow H\) is a group homomorphism and a is an element in G, \(a \in G\).
The order of a, a(o) is finite.