Let G be a group, and let xeG. How are o(x) and o(x) related? Prove your assertion
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question

Transcribed Image Text:Let G be a group, and let xeG. How are o(x) and o(x) related? Prove your
assertion
Expert Solution
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Step 1
According to the given conditions:
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it is needed to assert how o (x) and o(x") ar"
Step 2
Now, assume that order of element and its inverse are different:

Step 3
Now, consider the first equation:
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xe
m
multiply both side of equation by x" to get:
(x")(x)=e(xm)
e x
-m
x)o(x)
n<m.A)"
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Solved in 5 steps with 5 images
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