Element of Finite Group is of Finite Order/Proof 2
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Theorem
In any finite group, each element has finite order.
Proof
Follows as a direct corollary to the result Powers of Infinite Order Element.
$\blacksquare$
Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 38.3$ Period of an element