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Degrees of irreducible characters and normal $ p$-complements


Author: Ya. G. Berkovich
Journal: Proc. Amer. Math. Soc. 106 (1989), 33-35
MSC: Primary 20C15
DOI: https://doi.org/10.1090/S0002-9939-1989-0952314-X
MathSciNet review: 952314
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Abstract: John Tate [1] proved that if $ P \in {\mathbf{S}}{\text{y}}{{\text{l}}_p}(G)$, $ H$ is a normal subgroup of a finite group $ G$ and $ P \cap H \leq \Phi (P)$ ( $ \Phi (G)$ is the Frattini subgroup of $ G$) then $ H$ has a normal $ p$-complement. We prove in this note that Tate's theorem has nice character-theoretic applications.


References [Enhancements On Off] (What's this?)

  • [1] J. Tate, Nilpotent quotient groups, Topology 3 (1964), 109-111. MR 0160822 (28:4032)
  • [2] J. G. Thompson, Normal $ p$-complements and irreducible characters, J. Algebra 14 (1970), 129-134. MR 0252499 (40:5719)
  • [3] J. G. Thompson, Normal $ p$-complements for finite groups, Math. Z. 72 (1960), 332-354. MR 0117289 (22:8070)
  • [4] P. Roquette, Über die Existenz von Hall-Komplementen in endlichen Gruppen, J. Algebra 1 (1964), 342-346. MR 0170942 (30:1177)
  • [5] Ya. G. Berkovich and E. M. Zhmud', Characters of finite groups, Part II (to appear).

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DOI: https://doi.org/10.1090/S0002-9939-1989-0952314-X
Article copyright: © Copyright 1989 American Mathematical Society

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