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A conjecture on the number of conjugacy classes in ap-solvable group

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Abstract

IfG is ap-solvable group, it is conjectured that k(G/O P (G) ≤ |G| p ′. The conjecture is easily obtained for solvable groups as a consequence of R. Knörr’s work on the k(GV) problem. Also, a related result is obtained: k(G/F(G)) is bounded by the index of a nilpotent injector ofG.

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References

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  3. R. Knörr,On the number of characters in a p-block of a p-solvable group, Illinois Journal of Mathematics28 (1984), 181–210.

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Authors and Affiliations

  1. Department d'Algebra, Facultat de Matematiques, Universitat de Valencia, 46100, Burjassot, Valencia, Spain

    M. J. Iranzo, Gabriel Navarro & F. Pérez Monasor

Authors
  1. M. J. Iranzo
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  2. Gabriel Navarro
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  3. F. Pérez Monasor
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Additional information

Research partially supported by DGICYT.PB 90-0414-C02-01.

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Iranzo, M.J., Navarro, G. & Monasor, F.P. A conjecture on the number of conjugacy classes in ap-solvable group. Israel J. Math. 93, 185–188 (1996). https://doi.org/10.1007/BF02761101

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  • DOI: https://doi.org/10.1007/BF02761101

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