Show that if H₁ is a subgroup of G₁ and H₂ is a subgroup of G2, then H₁ X H₂ is a subgroup ofG₁ x G₂. Let H be a subgroup of G₁ x G₂. Is H necessarily of the form H₁ x H₂?

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Answered: Show that if H₁ is a subgroup of G₁ and…

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 19E: 19. With and as in Exercise 18, prove that is a subgroup of . Exercise18: 18. If is a...

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Show that if H₁ is a subgroup of G₁ and H₂ is a subgroup of G2, then H₁ × H₂ is a subgroup of G₁ × G₂. Let H be a subgroup of G₁ × G₂. Is H necessarily of the form H₁ × H₂?