Search results for "McKay conjecture"

showing 2 items of 2 documents

Character sums and double cosets

2008

Abstract If G is a p-solvable finite group, P is a self-normalizing Sylow p-subgroup of G with derived subgroup P ′ , and Ψ is the sum of all the irreducible characters of G of degree not divisible by p, then we prove that the integer Ψ ( P ′ z P ′ ) is divisible by | P | for all z ∈ G . This answers a question of J. Alperin.

Discrete mathematicsFinite groupAlgebra and Number TheoryDegree (graph theory)Character theorySylow theoremsCommutator subgroupFinite groupsCombinatoricsCharacter (mathematics)IntegerDouble cosetsCosetCharacter theoryMcKay conjectureMathematicsJournal of Algebra
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McKay natural correspondences on characters

2014

Let [math] be a finite group, let [math] be an odd prime, and let [math] . If [math] , then there is a canonical correspondence between the irreducible complex characters of [math] of degree not divisible by [math] belonging to the principal block of [math] and the linear characters of [math] . As a consequence, we give a characterization of finite groups that possess a self-normalizing Sylow [math] -subgroup or a [math] -decomposable Sylow normalizer.

Discrete mathematicsFinite groupAlgebra and Number TheoryDegree (graph theory)self-normalizing Sylow subgroup20C15Sylow theoremsBlock (permutation group theory)Characterization (mathematics)Centralizer and normalizerPrime (order theory)$p$-decomposable Sylow normalizerCombinatoricsMathematics::Group TheoryMcKay conjecture20C20MathematicsAlgebra & Number Theory
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