6. a) Prove that S, is not abelian for all n23. b) Prove that A, is not abelian for all n24. Ay =4!/2

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Q: 64. Express Ug(72)and U4(300)as an external direct product of cyclic groups of the form Zp

A: see my attachments

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Q: 52

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Q: (а) (Q, +) (b) (Zs, ·)

A: (a)(ℚ,+)(b)(ℤ8,.)

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A: Since it has associative property (ab) ^2  = a^2b^2

Q: - frele thab G=xK is abelian ifP both of HiK are abelian -Does Z12 Hxk where, H-Só, ū 83

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