3.5.6 Exercise 3.5.6 Show that if H is a normal subgroup of G, then the map : G→ G/Hdefined by T(g) = gH is an onto group homomorphism. This map is often called the naturalprojection of G onto G/H.

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Answered: Exercise 3.5.6 Show that if H is a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 21E

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Exercise 3.5.6 Show that if H is a normal subgroup of G, then the map n:G→ G/H defined by T(g) = gH is an onto group homomorphism. This map is often called the natural projection of G onto G/H.