Gokul Asked a Question
November 19, 2020 10:15 pmpts 30 pts
Which of the following is false? fa) Any abelian group of order 27 is cyclic (b) Any abelian group of order 14 is cyelic c) Any abelian group of order 21 is cyclic (d) Any abelian group of order 30 is cyclic
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  • Gokul
    ok😊
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  • Anuj s. Best Answer
    (b), (c), (d) are true. By the main theorem on finite abelian groups, they are direct products of cyclic groups, necessarily of orders 2 and 7 (b), 3 and 7 (c), and 2, 3, 5 (d). Di...
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  • Anuj s. thankyou
    a) is false, because 27 is divided by 9, which is 3 * 3. For any number that is divided by the square of a prime, there is an abelian group that is not cyclic. In this case, the gr...
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