In mathematics, specifically group theory, Frobenius's theorem states that if n divides the order of a finite group G, then the number of solutions of x n = 1 is a multiple of n. It was introduced by Frobenius (1903).
Related is Frobenius's conjecture (since proved, but not by Frobenius), which states that if the preceding is true, and the number of solutions of x n = 1 equals n, then the solutions form a normal subgroup.