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Solutions To Mathematics Textbooks/Topics In Algebra (2nd) 9788126510184/Group Theory/Page 35
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As and are abelian, .
Similarly progressing we obtain
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Let be a group of elements, where is a natural number.
Except there is an odd number of elements in .
Those elements who's order is greater than 2 can be paired with their inverse.
Since we have started with an of number of elements,
we must end with at least one unpaired element that satisfies .