On a minimal counterexample to the Alperin-McKay conjecture. (English) Zbl 1237.20011

From the text: We prove the following Theorem. For a minimal counterexample \((G,B)\) to the Alperin-McKay conjecture, the following holds. (i) \(O_p(G)\) and \(O_{p'}(G)\) are both central in \(G\). In particular, the Fitting subgroup of \(G\) is a central subgroup of \(G\). (ii) \(G\) has a unique \(G\)-conjugacy class of components.


20C20 Modular representations and characters
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
Full Text: DOI


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