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A lower bound for the number of odd-degree representations of a finite group

A lower bound for the number of odd-degree representations of a finite group Let G be a finite group and P a Sylow 2-subgroup of G. We obtain both asymptotic and explicit bounds for the number of odd-degree irreducible complex representations of G in terms of the size of the abelianization of P. To do so, we, on one hand, make use of the recent proof of the McKay conjecture for the prime 2 by Malle and Späth, and, on the other hand, prove lower bounds for the class number of the semidirect product of an odd-order group acting on an abelian 2-group. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

A lower bound for the number of odd-degree representations of a finite group

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References (21)

Publisher
Springer Journals
Copyright
Copyright © Springer-Verlag GmbH Germany, part of Springer Nature 2021
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-020-02660-z
Publisher site
See Article on Publisher Site

Abstract

Let G be a finite group and P a Sylow 2-subgroup of G. We obtain both asymptotic and explicit bounds for the number of odd-degree irreducible complex representations of G in terms of the size of the abelianization of P. To do so, we, on one hand, make use of the recent proof of the McKay conjecture for the prime 2 by Malle and Späth, and, on the other hand, prove lower bounds for the class number of the semidirect product of an odd-order group acting on an abelian 2-group.

Journal

Mathematische ZeitschriftSpringer Journals

Published: Jan 5, 2021

Keywords: Finite groups; Odd-degree representations; Characters; Coprime action; Primary 20C15; 20D10; 20D05

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