Characters of odd degree

Malle, Gunter; Späth, Britta

doi:10.4007/annals.2016.184.3.6

Cited by 73 publications

(156 citation statements)

References 31 publications

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“…Furthermore,

InnDiag (S)

has a self‐normalising Sylow 2‐subgroup by [, Lemma 3.17]. By [, Lemma 21.14; , Lemma 7.5], we see that

{Irr}_{2^{'}} false(G false) = {Irr}_{2^{'}} false(B_{0} (G) false)

, where

G = {Sp}_{2 n} false(q false)

is the Schur cover for

S

. Thus, by Lemma , we have

{Irr}_{2^{'}} false(S false) = {Irr}_{2^{'}} false(B_{0} (S) false)

since

S = G / Z (G)

with

| Z (G) | = 2

.…”

Section: Passing From Almost Simple To Simple Groupsmentioning

confidence: 96%

Principal 2‐blocks and Sylow 2‐subgroups

Fry

Taylor

2018

Bull. London Math. Soc.

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Let G be a finite group with Sylow 2‐subgroup P⩽G. Navarro–Tiep–Vallejo have conjectured that the principal 2‐block of NGfalse(Pfalse) contains exactly one irreducible Brauer character if and only if all odd‐degree ordinary irreducible characters in the principal 2‐block of G are fixed by a certain Galois automorphism σ∈ Gal (double-struckQ ab /Q). Recent work of Navarro–Vallejo has reduced this conjecture to almost simple groups. We show that the conjecture holds for all relevant almost simple groups, thus establishing the conjecture for all finite groups.

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“…Furthermore,

InnDiag (S)

has a self‐normalising Sylow 2‐subgroup by [, Lemma 3.17]. By [, Lemma 21.14; , Lemma 7.5], we see that

{Irr}_{2^{'}} false(G false) = {Irr}_{2^{'}} false(B_{0} (G) false)

, where

G = {Sp}_{2 n} false(q false)

is the Schur cover for

S

. Thus, by Lemma , we have

{Irr}_{2^{'}} false(S false) = {Irr}_{2^{'}} false(B_{0} (S) false)

since

S = G / Z (G)

with

| Z (G) | = 2

.…”

Section: Passing From Almost Simple To Simple Groupsmentioning

confidence: 96%

Principal 2‐blocks and Sylow 2‐subgroups

Fry

Taylor

2018

Bull. London Math. Soc.

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“…The celebrated McKay conjecture on character degrees asserts that for any finite group G and prime p |Irr p ′ (G)| = |Irr p ′ (N G (P ))| (1.0.1) where Irr p ′ denotes the set of irreducible characters of degree prime to p and P is a Sylow p-subgroup of G. The reduction theorem proved by Isaacs-Malle-Navarro [IMN07] reduces this conjecture to the checking of the so-called inductive McKay condition for each finite simple group S and prime p (see [IMN07,§10]). The inductive McKay condition has been checked for many simple groups leaving open the cases of simple groups of Lie types B, D, 2 D, E 6 , 2 E 6 , E 7 for odd p and different from the characteristic of the group, see [Ma08a], [S12], [CS13], [MS16], [CS17a], [CS17b]. One of the main results of the present paper is the following.…”

Section: Introductionmentioning

confidence: 94%

Descent equalities and the inductive McKay condition for types B and E

Cabanes

Späth

2019

Advances in Mathematics

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We establish the inductive McKay condition introduced by Isaacs-Malle-Navarro [IMN07] for finite simple groups of Lie types B l (l ≥ 2), E 6 , 2 E 6 and E 7 , thus leaving open only the types D and 2 D. We bring to the methods previously used by the authors for type C [CS17b] some descent arguments using Shintani's norm map. This provides for types different from A, D, 2 D a uniform proof of the so-called global requirement of the criterion given by the second author in [S12, 2.12]. The local requirements from that criterion are verified through a detailed study of the normalizers of relevant Levi subgroups and their characters.

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“…McKay conjectured in his landmark paper that the number