Groups with Sharp Character of Type { - 1 , 1 , 3 }

Abstract

For a finite group G and its character χ, let Lχ be the image of χ on G- { 1 }. The pair (G, χ) is said to be sharp of type L if | G| = Π a∈L(χ(1) - a) , where L= Lχ. The pair (G, χ) is said to be normalized if the principal character of G is not an irreducible constituent of χ. In this paper, we study normalized sharp pairs of type L= { - 1 , 1 , 3 } proposed by Cameron and Kiyota in [J Algebra 115(1):125–143, 1988], under some additional hypotheses. © 2022, The Author(s) under exclusive licence to Iranian Mathematical Society.