Computations In Exercises 1 through 6, determine whether the binary operation gives a group structure on the given set. If no group results, give the first axiom in the order G₁, G₂, G3 from Definition 4.1 that does not hold. 1. Let be defined on Z by letting a*b = ab. 2. Let* be defined on 2Z = {2n|n € Z} by letting a b=a+b. 3. Let * be defined on R+ by letting a + b = √ab.

Computations In Exercises 1 through 6, determine whether the binary operation gives a group structure on the given set. If no group results, give the first axiom in the order G₁, G₂, G3 from Definition 4.1 that does not hold. 1. Let be defined on Z by letting ab = ab. 2. Let be defined on 2Z = {2n|n € Z} by letting a b=a+b. 3. Let * be defined on R+ by letting a + b = √ab.

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 8E: Exercises In Exercises, decide whether each of the given sets is a group with respect to the...

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