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Calculus and Beyond Homework Help
Subgroup of a Quotient is a Quotient of a Subgroup
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[QUOTE="Szichedelic, post: 4547987, member: 158623"] [h2]Homework Statement [/h2] I'm trying to prove the statement "Show that a subgroup of a quotient of G is also a quotient of a subgroup of G." [h2]Homework Equations[/h2] See below. [h2]The Attempt at a Solution[/h2] Let G be a group and N be a normal subgroup of G. Let H be a subgroup of the quotient G/N. Then, by the fourth isomorphism theorem, H is isomorphic to the subgroup of G of the form H/N. I'm wondering if I am done at this point... My teacher's statement is somewhat vague and I can't decide if by "quotient of a subgroup of G," he means G quotiented by ANOTHER normal subgroup or a quotient OF a subgroup of G. If it is the latter, than this problem is trivially true by the fourth isomorphism theorem. [/QUOTE]
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Subgroup of a Quotient is a Quotient of a Subgroup
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