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Asked Sep 19, 2019
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Complete the proof of the following proposition:
If x is an element of the order m in a group G and if, for a positive integer s, we have
xe then m divides s.
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Complete the proof of the following proposition: If x is an element of the order m in a group G and if, for a positive integer s, we have xe then m divides s.

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Expert Answer

Step 1

To prove the required divisibility property of the order m of an element 

Step 2

By definition, the order of an element x in a group G is the SMALLEST positive integer m such that x^m =e. 

Step 3

Problem statement (here we a...

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order(x) = mx = e,and k < m=k = 0; Now,x =e(given) To show, m divides

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