IJPAM: Volume 84, No. 5 (2013)

FINITE SOLVABLE GROUPS HAVING A UNIQUE
IRREDUCIBLE CHARACTER OF A GIVEN DEGREE

Venkata Rao Potluri
Department of Mathematics
Reed College
3203, SE Woodstock Blvd, Portland, OR 97202, Portland, USA


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

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DOI: 10.12732/ijpam.v84i5.4 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 84
Issue: 5