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 conjectur...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2021-08, Vol.298 (3-4), p.1559-1572
Main Authors: Hung, Nguyen Ngoc, Keller, Thomas Michael, Yang, Yong
Format: Article
Language:English
Subjects:
Group theory
Lower bounds
Mathematics
Mathematics and Statistics
Representations
Subgroups
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Summary: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.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-020-02660-z