Exercise 2.5.6 State whether each of the following statements is true or false and give a brief reason for your ansuer. (а) А суclic group can have only one generator. (b) Any Abelian group is cyclic. (c) The group G={a, b, c, d} of order 4 with the following multiplication table is cyclic. * a b d a bc badc cdb a d a d d a

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Q: Show that any group of order 3 is abelian.

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Q: If U(14) = , then U(14) is cyclic group generator by a) 5 b) 11 c) 4 d) None of the above

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Q: Which of the following is cyclic group? О а. Q O b. C О с. Z O d. R е. N

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Q: means a cyclic group but 3+i can't turn into 3-i with a positive integer exponent.

A: Please see the answer in next step.

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Q: please answer letter a only

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Q: (bläi) äbäi 2.5 3 Jlgull How many abelian groups of order the ?Z180 same as 30O 10 40 30 1.

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Q: (а) (Q, +) (b) (Zs, ·)

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