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Subgroup Finding with Given G and H Conditions

Find the values of G and H based on given conditions and evaluate the number of subgroups in Z7.

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Subgroup Finding with Given G and H Conditions

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  1. Find [G : H] if G = Z18 and H = <12>. • 1.5 (b) 3 • 6 (d) 9 • 12 (f) 18 • (g) None of the above

  2. Find [G : H] if G = Z30 and H = <24>. • 1.5 (b) 3 • 6 (d) 9 • 12 (f) 18 • (g) None of the above

  3. Find [G : H] if G = S5 and H = A5. • 1 (b) 2 • 5 (d) 10 • 60 (f) 120 • (g) None of the above

  4. Find [G : H] if G = S5 and H = <(2,5)>. • 1 (b) 2 • 5 (d) 10 • 60 (f) 120 • (g) None of the above

  5. Find [G : H] if G = S5 and H = <(3, 1, 4, 2)>. • 1 (b) 2 • 5 (d) 30 • 60 (f) 120 • (g) None of the above

  6. Find [G : H] if G = Z and H = 3Z. • 1 (b) 2 • 3 (d) 5 • 60 (f) Infinity • (g) None of the above

  7. How many subgroups does Z7 have? • 1 (b) 2 • 3 (d) 5 • 60 (f) Infinity • (g) None of the above

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