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Prove that if G is a group and a E G, then o(a- 1 ) = o(a)

Chapter 14, Problem 14.30

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QUESTION:

Prove that if G is a group and a E G, then o(a- 1 ) = o(a).

Questions & Answers

QUESTION:

Prove that if G is a group and a E G, then o(a- 1 ) = o(a).

ANSWER:

Step 1 of 2

Consider the given function is the cyclic subgroups of  as,

                                   

Compute the above cyclic subgroups of

                                                               

 

Further solving,

                                                           

 

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