This preview shows page 1. Sign up to view the full content.
Unformatted text preview: G of order 2 is odd. In particular, G must contain an element of order 2. 5. For x an element of G , where G is a group, show that x and x-1 have the same order. 6. Find elements A , B and C in D 4 (the group of symmetries of the square) such that AB = BC but A 6 = C . 7. Assume H is a nonempty subset of ( G,? ) which is closed under the binary operation on G and is closed under inverses, i.e., for all h and k H , hk and h-1 H . Prove that H is a group under the operation ? restricted to H . ( H is called a subgroup of G ) 8. Let G be a group, and let y G have order m . If m = dt for some d 1, prove that y t has order d ....
View Full Document
- Spring '11