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Number of nth roots is a multiple of n

This article states a result of the form that one natural number divides another.
View other divisor relations |View congruence conditions

Contents

Statement

Suppose G is a finite group and n is any natural number dividing the order of G. Then, the size of the set:

\{g \in G \mid g^n = e \}

is a multiple of n.

Note that since the identity element is itself in this set, the size of the set is at least n.

Related facts

Facts used

Proof

The proof follows from fact (1); in fact, the given statement is a special case of fact (1).