Let S be a nonempty finite set with a binary operation * that satisfies the associative law. Show that S is a group if a * b = a * c implies b = c and a *c = b * c implies a = b for all a, b, c E S. What can you say if S is infinite?
Let S be a nonempty finite set with a binary operation * that satisfies the associative law. Show that S is a group if a * b = a * c implies b = c and a *c = b * c implies a = b for all a, b, c E S. What can you say if S is infinite?
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.1: Definition Of A Group
Problem 14E: In Exercises 114, decide whether each of the given sets is a group with respect to the indicated...
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