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Award ID contains: 1665014

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  1. ; ; ; (, International Mathematics Research Notices)
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  2. ; (, Bulletin of the London Mathematical Society)
  3. ; ; (, Journal of the European Mathematical Society)
    Accepted Manuscript Full Text Available
  4. ; ; ; (, Journal of Algebra)
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  5. ; ; (, Proceedings of the London Mathematical Society)
  6. ; (, Mathematical Proceedings of the Cambridge Philosophical Society)
    Abstract The classical Itô-Michler theorem on character degrees of finite groups asserts that if the degree of every complex irreducible character of a finite group G is coprime to a given prime p , then G has a normal Sylow p -subgroup. We propose a new direction to generalize this theorem by introducing an invariant concerning character degrees. We show that if the average degree of linear and even-degree irreducible characters of G is less than 4/3 then G has a normal Sylow 2-subgroup, as well as corresponding analogues for real-valued characters and strongly real characters. These results improve on several earlier results concerning the Itô-Michler theorem. 
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