- In This Exercise You Will Classify All Non Abelian Groups Of Order 8 Up To Isomorphism Let G Be A Non Abelian Group Of 1 (72.35 KiB) Viewed 31 times
In this exercise, you will classify all non-abelian groups of order 8 up to isomorphism. Let G be a non-abelian group of
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In this exercise, you will classify all non-abelian groups of order 8 up to isomorphism. Let G be a non-abelian group of
In this exercise, you will classify all non-abelian groups of order 8 up to isomorphism. Let G be a non-abelian group of order 8. 1. Prove that G has an element x of order 4 . 2. Let y∈G\⟨x⟩. Prove that G={e,x,x2,x3,y,xy,x2y,x3y}. 3. Prove that either y2=e or y2=x2, and either yx=x2y or yx=x3y. 4. Prove that if y2=e, then yx=x3y and G is isomorphic to the dihedral group D4 of order 8 . 5. Prove that if y2=x2, then yx=x3y and G is isomorphic to the dicyclic group Dic 2 of order 8 . (The dicyclic group Dic2 of order 8 is equal to the quaternion group Q8⋅)
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