10. In the group S5, let 0 = (1 2 3)(45) 3 and H= < o>....

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10. In the group S5, let 0 = (1 2 3)(45) 3 and H=< o>. (a) List the elements of H; each written as a product of disjoint cycles. (b) Using Langrange's Theorem, find the index of H in S5: [S5 : H]. (c) Find the left coset of H which contains (1 2 3). (Each element of the coset should be written in the standard way as a product of disjoint cycles.) 10. In the group S5, let 0 = (1 2 3)(45) 3 and H=< o>. (a) List the elements of H; each written as a product of disjoint cycles. (b) Using Langrange's Theorem, find the index of H in S5: [S5 : H]. (c) Find the left coset of H which contains (1 2 3). (Each element of the coset should be written in the standard way as a product of disjoint cycles.)

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a The elements of H are e 12345 13245 12314531245 b By Lagra... View the full answer