2010
DOI: 10.1515/jgt.2010.024
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On p-Brauer characters of p′-degree and self-normalizing Sylow p-subgroups

Abstract: Abstract. Let G be a finite group and p > 2 a prime. We show that a Sylow p-subgroup of G is self-normalizing if and only if G has no non-trivial irreducible p-Brauer character of degree not divisible by p.

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Cited by 14 publications
(10 citation statements)
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“…Although the equivalence of (a) and (c) is elementary, the equivalence between (a) and (b) is much deeper and requires the classification of finite simple groups. In addition, a p odd version of part of the above result can be obtained if we replace Q by Q p , the cyclotomic field [27].…”
Section: Brauer Charactersmentioning
confidence: 91%
“…Although the equivalence of (a) and (c) is elementary, the equivalence between (a) and (b) is much deeper and requires the classification of finite simple groups. In addition, a p odd version of part of the above result can be obtained if we replace Q by Q p , the cyclotomic field [27].…”
Section: Brauer Charactersmentioning
confidence: 91%
“…We would like to mention here that recently (see [17]) it has been proved that for a general finite group G and p an odd prime the conditions a) and b) in Proposition 3.5 are equivalent.…”
Section: Introductionmentioning
confidence: 93%
“…We would like to mention here that recently (see [17]) it has been proved that for a general finite group G and p an odd prime the conditions a) and b) in Proof: Assume that part a) holds. Let V denote the F G-module affording ϕ and let W be the F J-module affording γ.…”
Section: Introductionmentioning
confidence: 99%
“…A basic fact [18,13.1] about simple kG(q)-modules is that they are the restrictions of certain simple rational modules for G(k), the ambient Chevalley group over k. By this we mean that G(k) has an endomorphism σ, such that G(q) is the subgroup of fixed points ( [18, 12.4]). Further, we may assume that the subgroups T and B are σ-stable and denote by T (q) and B(q) the subgroups of T and B fixed by σ. G(k) is a simply connected algebraic group, since G(q) is universal.…”
Section: 2mentioning
confidence: 99%
“…The simple modules in case (A ′ ) were brought to our attention by Pham Huu Tiep, who asked about their dimensions as well as those in (B), (D) and (A) in connection with work on heights of characters in blocks [13]. A. Kleschchev has informed us that Theorem 1.4 is included among the results in the Ph.D. thesis (1992, Moscow State University) of A. Adamovich, where the Weyl modules with highest weight equal to the sum of two fundamental weights are treated.…”
Section: Introductionmentioning
confidence: 99%