Dade's inductive conjecture for the Ree groups of type \(G_2\) in the defining characteristic
Dade's inductive conjecture is a generalization of the Alperin-McKay conjectures, and relates the numbers of characters, with certain properties of a group \(G\), to numbers of characters of certain \(p\)-local subgroups, via a complicated formula. Using the Classification Theorem for Finite Simple Groups, one might hope to verify the conjecture by first reducing to simple groups, and then checking the simple groups. The amount of calculation involved in such checking is however formidable, and only a few cases, including at least ten of the sporadic simple groups as well as the Suzuki groups and the Tits group, and the small Ree groups in non-defining characteristic, have been treated so far. The present paper is devoted to the verification of Dade's inductive conjecture for the small Ree groups in defining characteristic, that is \(p=3\).
scientific article; zbMATH DE number 1441825
scientific article