Even degree characters in principal blocks

2017/10/04 by Giannelli, Eugenio, Malle, Gunter, Vallejo, Carolina
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1710.01596

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 p=7 and the group is M₂₂. As a consequence we deduce that if p≠ 7 or if M₂₂ is not a composition factor of a group G, then the condition above is equivalent to G/O_p'(G) having odd order.

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