Let G be a nonempty finite set with an associative binary operation such that for all a,
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Let G be a nonempty finite set with an associative binary operation such that for all a, b, c ϵ G ab= ac ⇒ b = c and ba = ca ⇒ b = c. Then G is a group. Show that this conclusion may be false if G is infinite.
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ANSWER Proof for the case where G is finite We need to show that G satisfies the four group axioms c...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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