The subset D = {(m, n) | m, ne Z and 2m+ n = 0} of the group Z x ZZ under addition
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.2: Properties Of Group Elements
Problem 15E: 15. Prove that if for all in the group , then is abelian.
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Question
Prove or disprove the subset is a subgroup of the given group. If it is not a subgroup, is your subset closed or does it contain inverses? Prove your answers.
![The subset D
= {(m, n) | m, ne Z and 2m+ n = 0} of the group Z x ZZ under addition](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F545e4110-447f-42e0-86d8-f710095b2322%2Fa51449e6-6e26-406c-9e3f-c321e831b475%2Fa51efjt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The subset D
= {(m, n) | m, ne Z and 2m+ n = 0} of the group Z x ZZ under addition
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