JournalsrmiVol. 38, No. 3pp. 1013–1028

A McKay bijection for projectors

  • Gabriel Navarro

    Universitat de València, Burjassot, Spain
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If F\mathfrak F is a saturated formation of groups, we define a canonical subset IrrF(G)\text{Irr}_{\mathfrak F'}(G) of the irreducible complex characters of a finite solvable group GG. If HH is an F\mathfrak F-projector of GG, we show that IrrF(G)=Irr(NG(H)/H)|\text{Irr}_{\mathfrak F'}(G)|=|\text{Irr}(\mathbf{N}_G(H)/H')|, where H=[H,H]H'=[H,H] is the derived subgroup of HH. In particular, if F\mathfrak F is the class of pp-groups, this reproves the solvable case of the celebrated McKay conjecture.

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Gabriel Navarro, A McKay bijection for projectors. Rev. Mat. Iberoam. 38 (2022), no. 3, pp. 1013–1028

DOI 10.4171/RMI/1294