Itô's Theorem

The dimension d of any irreducible representation of a group G must be a divisor of the index of each maximal normal Abelian subgroup of G.

Note that while Itô's theorem was proved by Noboru Itô, Ito's lemma was proven by Kiyoshi Ito.

See also

Abelian Group, Irreducible Representation, Subgroup

Explore with Wolfram|Alpha


More things to try:


Itô, N. "On the Degrees of Irreducible Representations of a Finite Group." Nagoya Math. J. 3, 5-6, 1951.Lomont, J. S. Applications of Finite Groups. New York: Dover, p. 55, 1993.

Referenced on Wolfram|Alpha

Itô's Theorem

Cite this as:

Weisstein, Eric W. "Itô's Theorem." From MathWorld--A Wolfram Web Resource.

Subject classifications