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 January 23rd, 2013, 09:20 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, 05:18 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, 08:20 AM #3 Newbie   Joined: Jan 2013 From: west bengal,india Posts: 22 Thanks: 0 Re: Equivalence Relation Thank u Tags equivalence, relation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post tom33 Algebra 3 January 17th, 2014 04:30 PM jrklx250s Real Analysis 3 December 7th, 2011 10:42 AM page929 Abstract Algebra 1 October 11th, 2010 12:33 PM Dontlookback Abstract Algebra 1 April 20th, 2010 11:52 AM tinynerdi Abstract Algebra 1 January 11th, 2010 09:24 AM

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