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Unformatted text preview: and O for the coset O D .12/ E D E .12/ consisting of odd permuta-tions. The subgroup E is the kernel of the sign homomorphism W S n ! f 1; 1 g . Since the product of two permutations is even if, and only if, both are even or both are odd, we have the following multiplication table for the two cosets of E : E O E E O O O E The products are taken in the sense mentioned previously; namely the product of two even permutations or two odd permutations is even, and the product of an even permutation with an odd permutation is odd. Thus the multiplication on the cosets of E reproduces the multiplication on the group f 1; 1 g . This is a general phenomenon: If N is a normal subgroup of a group G , then the set G=N of left cosets of a N in G has the structure of a group....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
- Fall '08