Understanding a proof of: In a finite group, the number of elements of ' order p is divisible by p−1.

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Breanna Fisher

2022-04-08

Understanding a proof of: In a finite group, the number of elements of ' order p is divisible by

p - 1

Jax Burns

Beginner2022-04-09Added 13 answers

Step 1
Let

0 (G) = p

a \in G - {1}

then the group generated by a is a subgroup of G, therefore its order divides p and therefore it is p (it cannot be 1 because then

a = 1

).
Because the order of an element is the order of the group it generates, we have that every element except for the identity is of order p.

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