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Journal of the London Mathematical Society 2006 73(2):493-505; doi:10.1112/S0024610705022556
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© The London Mathematical Society

Separating Characters by Blocks

Christine Bessenrodt, Gunter Malle and Jørn B. Olsson

Institut für Mathematik, Fakultät für Mathematik und Physik, Universität Hannover Welfengarten 1, D-30167 Hannover, Germany bessen{at}math.uni-hannover.de
Fachbereich Mathematik, Universität Kaiserslautern Postfach 3049, D-67653 Kaiserslautern, Germany malle{at}mathematik.uni-kl.de
Matematisk Institut, Københavns Universitet Universitetsparken 5, 2100 Copenhagen Ø, Denmark olsson{at}math.ku.dk

Received 10 December 2004. Revision received 25 May 2005.

We investigate the problem of finding a set of prime divisors of the order of a finite group, such that no two irreducible characters are in the same p-block for all primes p in the set. Our main focus is on the simple and quasi-simple groups. For results on the alternating and symmetric groups and their double covers, some combinatorial results on the cores of partitions are proved, which may be of independent interest. We also study the problem for groups of Lie type. The sporadic groups (and their relatives) are checked using GAP.


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