A reduction theorem for the McKay conjecture

By I. Isaacs, Gunter Malle, Gabriel Navarro. 2007

161 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/84c089b69a341c30d9fc57f358f1ab6b8bac3285

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Britta Spath
2. Gunter Malle
3. Pham Huu Tiep
4. Britta Spaeth
5. M. Cabanes
6. Gabriel Navarro
7. Jay Taylor

In Discrete Mathematics and Combinatorics

1. Gunter Malle
2. Britta Spath
3. Pham Huu Tiep
4. Gabriel Navarro
5. Britta Spaeth
6. M. Cabanes
7. Jay Taylor
8. Markus Linckelmann

In Electrical and Electronic Engineering

1. Britta Spath
2. Gunter Malle
3. Pham Huu Tiep
4. Gabriel Navarro

Citations in the corpus

• Extensions of unipotent characters and the inductive McKay condition (2008, background): “Then X is good for the prime p in the sense of [ 10 ].”
• A reduction theorem for the Alperin weight conjecture (2011, methodology): “We define now what it means for a finite non-abelian simple group X of order divisible by p to be “AWC-good” for p. This definition goes along the same lines as the definition of “McKay-good” in [ 19 ].”
• Equivariant character correspondences and inductive McKay condition for type A (2013, background): “-subgroup of Gand where, for any finite group H, one denotes by Irrℓ′(H) the set of irreducible (complex) characters whose degrees are prime to ℓ. The reduction theorem by Isaacs, Malle and Navarro in [IMN07] gives hope that this conjecture can be proved by use of the classification of the finite simpl”
• On the inductive Alperin–McKay and Alperin weight conjecture for groups with abelian Sylow subgroups (2014, background): “In the recent past, both conjectures have been reduced to certain (stronger) statements about finite simple groups [18, 25].”
• The inductive Alperin–McKay and Blockwise Alperin Weight conditions for blocks with cyclic defect groups and odd primes (2013, unknown): “ whose universal covering group has a cyclic Sylow p-subgroup. Then the inductive AM condition holds for S with respect to p, in particular Ssatisfies the inductive McKay conditions from Section 10 of [IMN07]. Note that according to Table 2.2 of [GLS3] this proves the inductive AM condition for group”
• A reduction theorem for the Alperin–McKay conjecture (2012, methodology): “In [18], the authors proved that the McKay conjecture holds for a prime p if all simple groups satisfy the now so-called inductive McKay condition for p.”
• Action of automorphisms on irreducible characters of symplectic groups (2016, background): “. The representation theory of finite groups is abound with many deep and fascinating conjectures nicknamed local/global conjectures; the paradigm of these is the McKay Conjecture. In a landmark paper [IMN07] Isaacs–Malle–Navarro showed that the McKay Conjecture holds for all finite groups if a list o”
• Height 0 characters of finite groups of Lie type (2007, methodology): “This has been done in [15] for example for the simple groups PSL2(q), and in [23] for alternating and sporadic groups.”