In a group (G, 0) the elements a and b commute.Also O (a) = m and O (b) = n, are prime to each%3Dother, then(&) O (a.b) = \m%3D(b) O (a.b) = Jmn%3D(c) O (a.b) = mn%3|(d) O (a.b)= L.C.M. of m and n

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Answered: In a group (G, 0) the elements a and b…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 13E: Exercises 13. For each of the following values of, find all subgroups of the group described in...

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In a group (G, 0) the elements a and b commute. Also O (a) = m and O (b) = n, are prime to each other, then %3D («) O (a.b) = /m %3D (b) O (a.b) = Jmn (c) O (a.b) = mn %3D (d) O (a.b) = L.C.M. of m and n