MATH 546 Midterm: MATH546 South Carolina 546 93 2 nospace
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1993: let = (1, 2, 3)(4, 5, 6) and = (3, 4, 5) be elements of s6 . Write 1 as the product of disjoint cycles: let h be a subgroup of sn for some n 2 . Prove that either every permutation in h is even or exactly half of the permutations in h are even: let h be a subgroup of the group g . Let a be a xed element of g and let. Prove that k is a subgroup of g : let a be a set, b be a subset of a , and b be an element of b . If your answer is no, then give a counterexample: let a be a set and b be an element of a . If your answer is yes, then prove the statement.
