Archiv der Mathematik

, Volume 78, Issue 6, pp 430–434

Character tables and Sylow normalizers

  • I. M. Isaacs
  • G. Navarro

DOI: 10.1007/s00013-002-8267-4

Cite this article as:
Isaacs, I. & Navarro, G. Arch. Math. (2002) 78: 430. doi:10.1007/s00013-002-8267-4


Let \( \mathcal{Q} \in \mathrm{Syl}_q (G) \), where G is a p-solvable group. We show that \( \mathbf{N}_{G}(\mathcal{Q}) \) is a p′-group if and only if each irreducible character of G of q′-degree is Brauer irreducible at the prime p. This result is generalized to \( \pi \)-separable groups, and one consequence, which can also be proved directly, is that the character table of a finite solvable group determines the set of prime divisors of the normalizer of a Sylow q-subgroup.

Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • I. M. Isaacs
    • 1
  • G. Navarro
    • 1
  1. 1.Mathematics Department, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, USA¶ e-mail:,¶ e-mail: navarro@math.wisc.eduUS

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