MATH 546 Midterm: MATH546 South Carolina 546 sp01 3 nospace
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Each of the other problems is worth 11 points: let = (1, 2, 3)(4, 5, 6) and = (3, 4, 5) be elements of s6 . Write 1 as the product of disjoint cycles: is the group (z . Why or why not: is the group (z . Why or why not: let a be a set and b be an element of a . If your answer is no, then give a counterexample: let a be a set, b be a subset of a , and b be an element of b . If your answer is yes, then prove the statement. If your answer is no, then give a counterexample. 2: let h be a subgroup of the nite group g . [x] = {y g | xy 1 h} . Prove that h and [x] have the same number of elements: let h be the subgroup {(1), (12), (13), (23), (123), (132)} of s4 .
