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.

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

Statement

Given an irreducible representation V of a finite group G and a maximal normal abelian subgroup A ⊆ 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.


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