Frobenius's theorem (group theory)

In mathematical group theory, Frobenius's theorem states that if n divides the order of a finite group G, then the number of solutions of xⁿ = 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 xⁿ = 1 equals n, then the solutions form a normal subgroup.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.