Abstract. It has been conjectured that PSL (2,q), the projective special linear group of 2x2 matrices over a field of order q, is the only non-solvable group satisfying the property that it has a unique irreducible complex character χ of degree m>1 and every other irreducible complex character is such that its degree is relatively prime to m. (Such a χ is a particular case of the Steinberg character of finite Chevalley groups.) In this paper, we consider finite solvable groups satisfying the above property and obtain a complete classification.

Received: October 10, 2012

AMS Subject Classification: 20C15

Key Words and Phrases: finite solvable groups, Chevalley groups, Steinberg character, irreducible complex characters

Download paper from here.