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RESEARCH PRODUCT
Sylow Normalizers and Brauer Character Degrees
Gabriel NavarroAntonio Beltránsubject
Set (abstract data type)Finite groupPure mathematicsAlgebra and Number TheoryBrauer's theorem on induced charactersCharacter (mathematics)Group (mathematics)If and only ifSylow theoremsMathematicsdescription
Suppose that G is a finite group. In this note, we show that a local condition about Sylow normalizers is equivalent to a global condition on the degrees of certain irreducible Brauer characters of G. Theorem A. Let G be a finite p; q-solvable group, and let Q ∈ SylqG and P ∈ SylpG. Then every irreducible p-Brauer character of G of q′degree has p′-degree if and only if NGQ is contained in some G-conjugate of NGP. Theorem A needs a solvability hypothesis. If p = 7, then the irreducible p-Brauer characters of the group G = PSL2; 27 have degrees 1; 13; 26; 28. If we set q = 2, then each q′-degree is also a p′-degree.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2000-07-01 | Journal of Algebra |