# A McKay bijection for projectors

### Gabriel Navarro

Universitat de València, Burjassot, Spain

## Abstract

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

## Cite this article

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

DOI 10.4171/RMI/1294