Itô's theorem

Itô's theorem is a result in the mathematical discipline of representation theory due to Noboru Itô. It 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. "Itô's Theorem". Wolfram Mathworld. Wolfram Research. Retrieved 6 November 2018.

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