Prove that exactly one of the non-abelian groups of order 8 is isomorphic to asemidirect product C4 x C₂, explicitly identifying which one it is.

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Answered: Prove that exactly one of the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 14E: 14. Let be an abelian group of order where and are relatively prime. If and , prove that .

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Prove that exactly one of the non-abelian groups of order 8 is isomorphic to a semidirect product C4 x C₂, explicitly identifying which one it is.