Let m and n be integers. By mZ+nZ we mean the set {a + b a € mZ,b ≤ nZ} of all sums of anelement of mZ and nZ, i.e., a typical element of the group looks like xm + yn for some integers x andy.(a) Show that mZ+nZ is a subgroup of Z.(b) Find a generator of the subgroup 12Z +21Z.

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Answered: Integers. set {a and nZ, i.e., a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 21E: Exercises 21. Suppose is a cyclic group of order. Determine the number of generators of for each...

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Integers. set {a and nZ, i.e., a typical element of the group looks like xm +yn for some integers and mZ+nZ is a subgroup of Z. erator of the subgroup 12Z + 21Z.