In a group (G, 0) the elements a and b commute. Also O (a) = m and O (b) = n, are prime to each %3D other, then (6) O (a.b) = Vm %3D (b) O (a.b) = Vmn %3D (c) O (a.b) = mn (d) O (a.b)= L.C.M. of m and n
In a group (G, 0) the elements a and b commute. Also O (a) = m and O (b) = n, are prime to each %3D other, then (6) O (a.b) = Vm %3D (b) O (a.b) = Vmn %3D (c) O (a.b) = mn (d) O (a.b)= L.C.M. of m and n
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 31E: 31. Prove statement of Theorem : for all integers and .
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![In a group (G, O) the elements a and b commute.
Also O (a) = n and O (b) = n, are prime to each
other, then
(a) O (a.b) = Vm
%3D
(b) O (a.b) = /mn
(c) O (a.b) = mn
%3D
(d) O (a.b)= L.C.M. of m and n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55b3ada2-c89a-4711-8eaa-038e5b4f2333%2F8930e2f8-5a62-4039-9873-da72acee92fb%2Ff7wqc6u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In a group (G, O) the elements a and b commute.
Also O (a) = n and O (b) = n, are prime to each
other, then
(a) O (a.b) = Vm
%3D
(b) O (a.b) = /mn
(c) O (a.b) = mn
%3D
(d) O (a.b)= L.C.M. of m and n
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