14 If G is any group and a, b, c E G, show that if a b = a* c, then b = c,*and if b* a = c * a, then b = c.

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Answered: 14 If G is any group and a, b, c E G,…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 37E

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#5. Thanks.
If G is a group and a1, a2,…, an shows that a1 * a2 *… * an is unique, regardless of the order in which the operations are performed.

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14 If G is any group and a, b, c E G, show that if a b = a* c, then b = c, * and if b* a = c * a, then b = c.