MATH 546 Midterm: MATH546 South Carolina 546 fe s10
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If possible: turn the problems in order (use as much paper as necessary), use only one side of each piece of paper, and leave 1 square inch in the upper left hand corner for the staple. If you forget some of these requests, don"t worry about it i will still grade your exam. No calculators or cell phones: state the first isomorphism theorem. Write everything that is necessary, but nothing extra: de ne kernel. Write everything that is necessary for your de nition to make sense, but nothing extra: de ne left coset. Write everything that is necessary for your de nition to make sense, but nothing extra: let : g g be a group homomorphism. Suppose that the kernel of consists of the identity element of g . Prove that is a one-to-one: de ne a one-to-one homomorphism from the unit circle group u to the general.
