Problem Set 10

(10 points)

(From Gallian)


Read Chapter 5 again.
pp. 113-115 #7, 17a,b,c, 19, 31, 36, 43
Read Chapter 6.
Answer the following questions:
1) What did you find most confusing?
2) Are there groups we have seen that you know to be isomorphic? How do you know?
3) Are there groups of the same size that you know not to be isomorphic? How do you know?
4) We mentioned in class that if two groups have elements of different orders, then they cannot be isomorphic. Why do you think that is? Do you think there is a mathematical proof of this?