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 January 23rd, 2013, 10:20 AM #1 Newbie   Joined: Jan 2013 From: west bengal,india Posts: 22 Thanks: 0 Equivalence Relation If H be a subgroup of G then prove that the relation R defined on G by aRb iff (a)^(-1).b €H for a,b€G is an equivalence Relation
 January 24th, 2013, 06:18 AM #2 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: Equivalence Relation We need R to be, 1. Reflexive : aRa is true because a * a^-1 = e belongs to H since H is a subgroup of G 2. Symmetric : assuming a * b^-1 belongs to H, (a * b^-1)^-1 = b * a^-1 belongs to H. Hence if aRb then bRa. 3. Transitive : If a * b^-1 & b * c^-1 belongs to H then (a * b^-1) * (b * c^-1) = a * c^-1 belongs to H. Hence, if aRb and bRc then aRc. Hence, R is an equivalence relation.
 February 11th, 2013, 09:20 AM #3 Newbie   Joined: Jan 2013 From: west bengal,india Posts: 22 Thanks: 0 Re: Equivalence Relation Thank u

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