, Volume 78, Issue 6, pp 430-434

Character tables and Sylow normalizers

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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.

Eingegangen am 7. 8. 2000