If G is a group and H is a subgroup of index 2 in G show that H is a normal subgroup of G.
If G is a group and H is a subgroup of index 2 in G show that H is a normal subgroup of G.
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 22E: 22. If and are both normal subgroups of , prove that is a normal subgroup of .
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show that H is a normal subgroup of G.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4653cf3-0b4e-4aab-966b-90803047b25b%2F57c57030-0c0c-45f9-ab6c-00462c107491%2Fi6b0ru_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If G is a group and H is a subgroup of index 2 in G
show that H is a normal subgroup of G.
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