Answered: If H is a subgroup of G, then H is a…

If H is a subgroup of G, then H is a normal subgroup in G if and only if H × A2021 is a normal subgroup in G × S2021. Please explain the steps in detail, thank you in advance.

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 22E: 22. If and are both normal subgroups of , prove that is a normal subgroup of .

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Question

If H is a subgroup of G, then H is a normal subgroup in G if and only if H × A₂₀₂₁ is a normal subgroup in G × S₂₀₂₁. Please explain the steps in detail, thank you in advance.

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