Bounding the number of p'-degree characters from below

Thomas Michael Keller; Yong Yang

doi:10.1515/forum-2024-0033

Article

Bounding the number of p'-degree characters from below

Thomas Michael Keller and Yong Yang

Published/Copyright: January 13, 2025

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From the journal Forum Mathematicum Volume 37 Issue 5

Abstract

Let G be a finite group of order divisible by a prime p and let P ∈ Syl p ⁡ ( G ) . We prove a recent conjecture by Hung stating that | Irr p ′ ⁡ ( G ) | ≥ exp ⁡ ( P / P ′ ) - 1 p - 1 + 2 ⁢ p - 1 - 1 . Let a ≥ 2 be an integer and suppose that p a does not exceed the exponent of the center of P. We also show that the number of conjugacy classes of elements of G for which p a is the exact p-part of their order is at least p a - 1 .

Keywords: Finite groups; conjugacy classes

MSC 2020: 20E45; 20D05

Communicated by Manfred Droste

Funding source: Simons Foundation

Award Identifier / Grant number: #918096

Award Identifier / Grant number: YY

Funding statement: Yong Yang was partially supported by a grant from the Simons Foundation (#918096, YY).

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Received: 2024-01-15

Revised: 2024-11-03

Published Online: 2025-01-13

Published in Print: 2025-06-01

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Articles in the same Issue

https://doi.org/10.1515/forum-2024-0033

Keywords for this article

Finite groups; conjugacy classes