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Unformatted text preview: Let G be the abelian group, and suppose the quotient group is G / H where H G . Since G is abelian, xy = yx for all x , y G . Therefore HxHy = Hxy = Hyx = HyHx for all x , y G . Since the general element of G / H is of the form Hx for some x G , it follows that G / H is abelian....
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This note was uploaded on 01/02/2012 for the course MATH 3124 taught by Professor Parry during the Fall '08 term at Virginia Tech.
 Fall '08
 PARRY
 Math, Algebra

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