Vol. 15, No. 7, 2021

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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.

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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