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4. Let G be a group, and let H be a subgroup of G. Show that if H contains the commutator subgroup of G, then H◄ G. (Hint: correspondence theorem.)

4. Let G be a group, and let H be a subgroup of G. Show that if H contains the commutator subgroup of G, then H◄ G. (Hint: correspondence theorem.)

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.4: Cosets Of A Subgroup
Problem 14E: Let H be a subgroup of a group G. Prove that gHg1 is a subgroup of G for any gG.We say that gHg1 is...
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4. Let G be a group, and let H be a subgroup of G. Show that if H contains the commutator subgroup of G, then H◄ G. (Hint: correspondence theorem.)
Transcribed Image Text:4. Let G be a group, and let H be a subgroup of G. Show that if H contains the commutator subgroup of G, then H◄ G. (Hint: correspondence theorem.)
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