MATH 546 Midterm: MATH546 South Carolina 546 f04 f
Document Summary
Write your answers as legibly as you can on the blank sheets of paper provided. Turn in your solutions in the order: problem 1, problem 2, . ; although, by using enough paper, you can do the problems in any order that suits you. When i nish, i will e-mail your grade to you. I will post the solutions on my website when the exam is nished: (7 points) state and prove cayley"s theorem, (7 points) apply the proof of cayley"s theorem to the element (1, 2, 3) of the group. What do you get: (7 points) let : g g be a group homomorphism. Prove that is one-to-one if and only if the kernel of is {id} : (7 points) give an example of a non-abelian group of order 16. A very short explanation will su ce: (7 points) give an example of an abelian, but non-cyclic, group of order 16.
