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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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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