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(6)(20 points) (a) Let G be a cyclic group of order n. Prove that for every...

(6)(20 points) (a) Let G be a cyclic group of order n. Prove that for every divisor dofn there is a subgroup of Ghaving order

(6)(20 points) (a) Let G be a cyclic group of order n. Prove that for every divisor dofn there is a subgroup of Ghaving order d. (b) Characterize all factor groups of Z70.
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cyclic group of order 18 din Ill there if Subgroup of order d Sd- Now Cyclic G if n group of order then G zu dIn Now then oflet H, be 1 Subgroup of older subgroups of orgen 2 H2 be be H₃ Subgroup of order 5 T 7 / Hu 11 ܒ ܀ H5 14 71 35 17 11 70 7) H

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