Degrees of irreducible characters and normal $p$-complements
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- by Ya. G. Berkovich PDF
- Proc. Amer. Math. Soc. 106 (1989), 33-35 Request permission
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
- John Tate, Nilpotent quotient groups, Topology 3 (1964), no. suppl, suppl. 1, 109–111. MR 160822, DOI 10.1016/0040-9383(64)90008-4
- John G. Thompson, Normal $p$-complements and irreducible characters, J. Algebra 14 (1970), 129–134. MR 252499, DOI 10.1016/0021-8693(70)90116-X
- John G. Thompson, Normal $p$-complements for finite groups, Math. Z 72 (1959/1960), 332–354. MR 0117289, DOI 10.1007/BF01162958
- Peter Roquette, Über die Existenz von Hall-Komplementen in endlichen Gruppen, J. Algebra 1 (1964), 342–346 (German). MR 170942, DOI 10.1016/0021-8693(64)90013-4 Ya. G. Berkovich and E. M. Zhmud’, Characters of finite groups, Part II (to appear).
Additional Information
- © Copyright 1989 American Mathematical Society
- 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