Answered: Let G1 and G2 be any two groups and θ :…

Let G1 and G2 be any two groups and θ : G1 → G2 be a group isomorphism. Let H1 ≤ G1. Prove that H2 = θ(H1) ≤ G2 and |G1 : H1| = |G2 : H2|

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let G1 and G2 be any two groups and θ : G1 → G2 be a group isomorphism.
Let H1 ≤ G1. Prove that H2 = θ(H1) ≤ G2 and
|G1 : H1| = |G2 : H2|.(10 marks)

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