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 S Show that is an equivalence relation if and only if S is a subgroup of G ...

First we will prove that if S is a subgroup of G then the relation defined by a b if and only if ab ...

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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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Algebra Graduate Texts In Mathematics 73

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