# (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 d. (b) Characterize all factor groups of Z70.

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(6)(20 points) (a) Let G be a cyclic group of order n. Prove that for every divisor d of n there is a subgroup of G having order d. (b) Characterize all factor groups of Z70 -

• ### ASAP PLEASE (6)(20 points) (a) Let G be a cyclic group of order n. Prove that...

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• ### (a) Let G be a cyclic group of order n. Prove that fo every divisor d...

(a) Let G be a cyclic group of order n. Prove that fo every divisor d of n there is a subgroup of G having order d. (b) Characterize all factor groups of Z70.

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• ### need help ASAP with 6 and 7. Thank You! (6)(20 points) (a) Let G be a...

need help ASAP with 6 and 7. Thank You! (6)(20 points) (a) Let G be a cyclic group of order n. Prove that for every divisor dof n there is a subgroup of Ghaving order d. (b) Characterize all factor groups of Z70. (7)(20 points) (a) State the Fundamental Theorem of Finitely Generated Abelian Groups. (b) List all abelian groups of order 2450 up to isomorphism. (c) Show every abelian group of order 2450 has an element of order 70.

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• ### (a) Let G be a group of order 4 with identity e. Show that G is either cyclic or a2-e for all (b)...

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