Unformatted text preview: a. Prove that congruence modulo H is an equivalence relation on G . b. Determine the equivalence class of x ∈ G . c. If H is the trivial subgroup, when are two elements of G congruent modulo H ? Exercise 5. Show that the distinct cosets of H = SL 2 ( R ) in G = GL 2 ( R ) are given by ± x 0 1 ² H with x ∈ R ....
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 Spring '10
 RyanDaileda
 Algebra, Sets, Equivalence relation, congruent modulo

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