Let S be a nonempty subset of a group G and define a relation on G by
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Let S be a nonempty subset of a group G and define a relation on G by a ∼ b if and only if ab-1 ϵ S. Show that ∼ is an equivalence relation if and only if S is a subgroup of G.
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First we will prove that if S is a subgroup of G then the relation defined by a b if and only if ab ...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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