1. Trinity Hall, University of Cambridge, Trinity Lane, CB21TJ, UK;2. FB Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany;3. ICMAT, Campus Cantoblanco UAM, C/ Nicolás Cabrera, 13-15, 28049 Madrid, Spain
Abstract:
We characterise finite groups such that for an odd prime p all the irreducible characters in its principal p-block have odd degree. We show that this situation does not occur in non-abelian simple groups of order divisible by p unless and the group is . As a consequence we deduce that if or if is not a composition factor of a group G, then the condition above is equivalent to having odd order.