Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let G be a group and let H and K be normal subgroups such that Hnk= G/H x G/K be the map o(g) = (Hg, Kg). : G Prove that is a group homomorphism. {e}. Let

Let G be a group and let H and K be normal subgroups such that Hnk= G/H x G/K be the map o(g) = (Hg, Kg). : G Prove that is a group homomorphism. {e}. Let

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.5: Normal Subgroups
Problem 21E: With H and K as in Exercise 18, prove that K is a normal subgroup of HK. Exercise18: If H is a...
See similar textbooks
icon
Related questions
Question
100%
Let G be a group and let H and K be normal subgroups such that HK = {e}. Let ø: G→G/H × G/K be the map (g) = (Hg, Kg). Prove that is a group homomorphism.
Transcribed Image Text:Let G be a group and let H and K be normal subgroups such that HK = {e}. Let ø: G→G/H × G/K be the map (g) = (Hg, Kg). Prove that is a group homomorphism.
Expert Solution
steps

Step by step

Solved in 3 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer