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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 orde

(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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ó. (@) n. and । <d Ln Dome tet ď patinfying n € Ge Let Ge= Lay be a finite group of ordern. Then o(a) = n and Gc= {a, a² ....(9) 70- 2 X 5 X 7 ~ 770 There i Za 625 Ø 7 only ne factor the one gooule in 2270 117.(a) statement Every finitely generated abolicam in inomorphic to a direct sum p- primary cyclic groupro Il/pk 2 (for pina bsubgroup of order 70 and Let H be the then 0(H) = 70 = 2X5 X7 and ged (2,5,7) - 1 then H 222 X 25 X 27 since ged (2,5,7}=1 t

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