Type: Article

A conjecture of Cameron and Kiyota on sharp characters with prescribed values

Journal: Communications in Algebra (00927872)Year: 2022Volume: 50Issue: Pages: 2731 - 2739

Abdollahi A.^aBagherian J.^aKhatami Bidgoli M.^a Shahbazi Z.Sobhani R.^a

a :University of Isfahan - IRAN(IR) - Isfahan

GreenDOI:10.1080/00927872.2021.2018594Language: English

Abstract

Let χ be a virtual (generalized) character of a finite group G and (Formula presented.) be the image of χ on (Formula presented.) The pair (Formula presented.) is said to be sharp of type L or L-sharp if (Formula presented.) If the principal character of G is not an irreducible constituent of χ, the pair (Formula presented.) is called normalized. In this paper, we first provide some counterexamples to a conjecture that was proposed by Cameron and Kiyota in 1988. This conjecture states that if (Formula presented.) is L-sharp and (Formula presented.) then the inner product (Formula presented.) is uniquely determined by L. We then prove that this conjecture is true in the case that (Formula presented.) is normalized, χ is a character of G, and L contains at least an irrational value. © 2022 Taylor & Francis Group, LLC.

Author Keywords

Character valuefinite groupsharp charactersharp pair