Counting characters in blocks of \(M_{22}\)
Dade's 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 have been treated so far. The present paper is devoted to the verification of Dade's conjecture for the sporadic simple group \(M_{22}\) and all its covering groups.
scientific article; zbMATH DE number 1019683
scientific article