Answered: Let D_8 = . Let S_3 be the symmetric…

Let D_8 = . Let S_3 be the symmetric group of degree 3. Let G = D8 x S3. Let H = x <(123)> and K = x <(123)> Is H a normal subgroup of G? What about K?

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 17E

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Question

Let D_8 = <a,b | a^4 = b^2 = e , ba = a^3b>. Let S_3 be the symmetric group of degree 3. Let G = D8 x S3.

Let H = <b> x <(123)> and K = <a> x <(123)>

Is H a normal subgroup of G? What about K?

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