Let G be a group and let H and K be normal subgroups such that HnK={e}. Let : G→G/HxG/K be the map (g) = (Hg, Kg). Prove that the kernel of ois {e}.
Let G be a group and let H and K be normal subgroups such that HnK={e}. Let : G→G/HxG/K be the map (g) = (Hg, Kg). Prove that the kernel of ois {e}.
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 4E: 4. Prove that the special linear group is a normal subgroup of the general linear group .
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![Let G be a group and let H and K be normal subgroups such that HnK={e}. Let
: G→G/HxG/K be the map (g) = (Hg, Kg).
Prove that the kernel of ois {e}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2844e9b7-fdae-4ffb-b3b7-8f54bdb6d500%2F4bb67705-aaba-48e8-9688-a650b12d9292%2F9u95q4p_processed.png&w=3840&q=75)
Transcribed Image Text:Let G be a group and let H and K be normal subgroups such that HnK={e}. Let
: G→G/HxG/K be the map (g) = (Hg, Kg).
Prove that the kernel of ois {e}.
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