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.

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