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Using the Third Isomorphism Theorem, or otherwise, prove that if H₁ and H₂ are subgroups of an abelian group G, then |H₁ H₂| = |H₁||H₂| |H₁ H₂| Indicate clearly in your answer where, and how, you make use of the fact that G is abelian.

Using the Third Isomorphism Theorem, or otherwise, prove that if H₁ and H₂ are subgroups of an abelian group G, then |H₁ H₂| = |H₁||H₂| |H₁ H₂| Indicate clearly in your answer where, and how, you make use of the fact that G is abelian.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 6TFE: True or false Label each of the following statements as either true or false, where is subgroup of...
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Using the Third Isomorphism Theorem, or otherwise, prove that if H₁ and H₂ are subgroups of an abelian group G, then |H₁ H₂| = |H₁||H₂| |H₁ H₂| Indicate clearly in your answer where, and how, you make use of the fact that G is abelian.
Transcribed Image Text:Using the Third Isomorphism Theorem, or otherwise, prove that if H₁ and H₂ are subgroups of an abelian group G, then |H₁ H₂| = |H₁||H₂| |H₁ H₂| Indicate clearly in your answer where, and how, you make use of the fact that G is abelian.
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