If r is a divisor of m and s is a divisor of n, find a subgroup of Z, O Z, that is isomorphic to Z, O Z,.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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If r is a divisor of m and s is a divisor of n, find a subgroup of Z, O
Z, that is isomorphic to Z, O Z,.
Transcribed Image Text:If r is a divisor of m and s is a divisor of n, find a subgroup of Z, O Z, that is isomorphic to Z, O Z,.
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Step 1

Let  Algebra homework question answer, step 1, image 1and Algebra homework question answer, step 1, image 2.

we know that subgroup ,Algebra homework question answer, step 1, image 3is cyclic of order m which implies Z is isomorphic to Z .

Also the subgroup, Algebra homework question answer, step 1, image 4is cyclic of order n which implies Z n is isomorphic to Z s .

Suppose, G 1 ,G 2 , H 1 ,H 2  are subgroups such that G 1 ≤ Hand G 2 ≤ H2 , then Algebra homework question answer, step 1, image 5.

Thus, Algebra homework question answer, step 1, image 6, that is Algebra homework question answer, step 1, image 7 is subgroup of Algebra homework question answer, step 1, image 8.

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