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Using the first isomorphism theorem, how would you prove that G/K is isomorphic to G. I already know f(z) = z^4 is a group homomorphism and the kernel of f is K= {-i, i, 1,-1}.

Using the first isomorphism theorem, how would you prove that G/K is isomorphic to G. I already know f(z) = z^4 is a group homomorphism and the kernel of f is K= {-i, i, 1,-1}.

Elements Of Modern Algebra
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 19E: Find the order of each of the following elements in the multiplicative group of units . for for ...
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Using the first isomorphism theorem, how would you prove that G/K is isomorphic to G.

I already know f(z) = z^4 is a group homomorphism and the kernel of f is K= {-i, i, 1,-1}.

Let G be the subset of C given by {e²i¹ | x = R} with multiplication as group operation. (This is called the circle group).
Transcribed Image Text:Let G be the subset of C given by {e²i¹ | x = R} with multiplication as group operation. (This is called the circle group).
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