1. ## abstract algebra (group)

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...

2. Originally Posted by hayuning

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...

Fine: what've you done so far in each question?

Tonio

3. Originally Posted by hayuning
This one should be cake... $A=\{e\}$??