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?

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?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.4: Cosets Of A Subgroup

Problem 12E: Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order...

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Question

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?

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