McKay bijections for symmetric and alternating groups

Giannelli, Eugenio

doi:10.2140/ant.2021.15.1809

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McKay bijections for symmetric and alternating groups

Eugenio Giannelli

Vol. 15 (2021), No. 7, 1809–1835

DOI: 10.2140/ant.2021.15.1809

Abstract

We study fields of values of the restriction to Sylow subgroups of irreducible characters of the normalizers of Sylow subgroups in symmetric and alternating groups. As an application, we show that these classes of groups admit a McKay bijection that respects fields of values and restriction to Sylow subgroups.

Keywords

character theory, Sylow restriction, symmetric groups

Mathematical Subject Classification

Primary: 20C15, 20C30

Milestones

Received: 20 July 2020

Revised: 10 December 2020

Accepted: 19 January 2021

Published: 1 November 2021

Authors

Eugenio Giannelli
Dipartimento di Matematica e Informatica “Ulisse Dini” Università degli Studi di Firenze Florence Italy

Vol. 15, No. 7, 2021