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**hayuning** Someone please help me... I don't even understand.

1. Give an example of group G and two subgroup A, B of G such that AB is a subgroup of G

2. Prove that (1 2) cannot be written as the product of disjoint 3 cycles

3. 1. if G has no proper subgrup, prove that G is cyclic

4. Express as the product of disjoint cycles and find the order

a. (1 2 3 5 7) (2 4 7 6)

b. (1 2) ( 1 3) ( 1 4)

c. (1 2 3 4 5) ( 1 2 3 4 6) (1 2 3 4 7)

d. ( 1 2 3) (1 3 2)

I would be very thankful if someone could help me..please...