Even degree characters in principal blocks

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...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2019-02, Vol.223 (2), p.900-907
Main Authors: Giannelli, Eugenio, Malle, Gunter, Vallejo Rodríguez, Carolina
Format: Article
Language:English
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Summary: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/Op′(G) having odd order.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2018.05.004