Itô's theorem
{{About|the result in representation theory|the result in stochastic calculus|Itô's lemma}}
{{short description|Math theorem in the field of representation theory}}
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 {{mvar|V}} of a finite group {{mvar|G}} and a maximal normal abelian subgroup {{math|A ⊆ G}}, the dimension of {{mvar|V}} must divide {{math|[G : A]}}.
References
- {{cite book |last1=James |first1=Gordon |authorlink2=Martin Liebeck |last2=Liebeck |first2=Martin |page=[https://archive.org/details/representatiosch00jame/page/n256 247] |title=Representations and Characters of Groups |year=1993 |url=https://archive.org/details/representatiosch00jame |url-access=limited |publisher=Cambridge University Press |isbn=0-521-44590-6 }}
- {{cite web |last1=Weisstein |first1=Eric |title=Itô's Theorem |url=http://mathworld.wolfram.com/ItosTheorem.html |website=Wolfram Mathworld |publisher=Wolfram Research |access-date=6 November 2018}}
Category:Theorems in representation theory
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