Itô's theorem

This article is about the result in representation theory. For the result in stochastic calculus, see Itô's lemma.

In representation theory, Itô's theorem generalizes the well-known result that the dimension of an irreducible representation of a group must divide the order of that group.

Statement

Given an irreducible representation $V$ of a finite group $G$ and a maximal normal abelian subgroup $A\subseteq G$, the dimension of $V$ must divide $[G:A]$.

References

• James, Gordon; Liebeck, Martin (1993). Representations and Characters of Groups. Cambridge University Press. p. 247. ISBN 0-521-44590-6.

• Weisstein, Eric W. "Itô's Theorem". MathWorld. Retrieved 5 August 2026.