Week 11

Question 1

Prove

Answer 1

Question 2

Prove

Answer 2

Question 3

Prove

Answer 3

Question 4

Prove

Answer 4

Question 5

Prove

Answer 5

This means that, up to isomorphism, there are only 2 distinct groups of each order 4,9,25,49 both of which are Abelian

Question 6

For positive prime integer p, a p group is?

Answer 6

Question 7

Define a Sylow p-subgroup

Answer 7

Question 8

Sylow theorem

Answer 8

Question 9

Prove

Answer 9

Question 10

Prove

Answer 10

Question 11

Prove

Answer 11

Question 12

Prove

Answer 12

Question 13

Prove

Answer 13