If you let G and H be two groups and consider the product group G x H and let K be the subset of G x H given by K ={(g,e_H) | g ∈ G}. How would you prove that (G x H) / K is isomorphic to H using the 1st isomorphism theorem? I was given a hint to start with a map f: G × H -> H that sends (g, h) to h

If you let G and H be two groups and consider the product group G x H and let K be the subset of G x H given by K ={(g,e_H) | g ∈ G}. How would you prove that (G x H) / K is isomorphic to H using the 1st isomorphism theorem? I was given a hint to start with a map f: G × H -> H that sends (g, h) to h

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 20E: For each a in the group G, define a mapping ta:GG by ta(x)=axa1. Prove that ta is an automorphism of...

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