(5) Let G be a group. Let H be a subgroup of G and K be a normal subgroup of G. Prove that HK is a subgroup of G.
(5) Let G be a group. Let H be a subgroup of G and K be a normal subgroup of G. Prove that HK is a 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 18E: 18. If is a subgroup of , and is a normal subgroup of , prove that .
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subgroup of G. Prove that HK is a subgroup of G.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe591e3e-c1e9-4180-ad99-642a1f427277%2F2da1b0ad-34d3-4d6c-a0b8-0fd392d35198%2Fnpvii4_processed.png&w=3840&q=75)
Transcribed Image Text:(5) Let G be a group. Let H be a subgroup of G and K be a normal
subgroup of G. Prove that HK is a subgroup of G.
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