Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Let G be a group, and let xeG. How are o(x) and o(x) related? Prove your assertion
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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:

let G be a group and let xe G, it is needed to assert how o (x) and o(x") ar
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Step 2

Now, assume that order of element and its inverse are different:

= e ) let o (x)mx"- o(x1)n(x) e.)
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Step 3

Now, consider the first equation:

o(x)m 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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