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Nilpotent and abelian Hall subgroups in finite groups


Authors: Antonio Beltrán, María José Felipe, Gunter Malle, Alexander Moretó, Gabriel Navarro, Lucia Sanus, Ronald Solomon and Pham Huu Tiep
Journal: Trans. Amer. Math. Soc. 368 (2016), 2497-2513
MSC (2010): Primary 20D20; Secondary 20C15, 20D05, 20G40
Published electronically: July 10, 2015
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Abstract: We give a characterization of the finite groups having nilpotent or abelian Hall $ \pi $-subgroups that can easily be verified using the character table.


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Antonio Beltrán
Affiliation: Departamento de Matemáticas, Universidad Jaume I, 12071 Castellón, Spain
Email: abeltran@mat.uji.es

María José Felipe
Affiliation: Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46022 Valencia, Spain
Email: mfelipe@mat.upv.es

Gunter Malle
Affiliation: FB Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany
Email: malle@mathematik.uni-kl.de

Alexander Moretó
Affiliation: Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, Spain
Email: alexander.moreto@uv.es

Gabriel Navarro
Affiliation: Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, Spain
Email: gabriel.navarro@uv.es

Lucia Sanus
Affiliation: Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, Spain
Email: lucia.sanus@uv.es

Ronald Solomon
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Email: solomon@math.ohio-state.edu

Pham Huu Tiep
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Email: tiep@math.arizona.edu

DOI: https://doi.org/10.1090/tran/6381
Received by editor(s): October 30, 2013
Received by editor(s) in revised form: January 10, 2014, and January 20, 2014
Published electronically: July 10, 2015
Additional Notes: The research of the first, second, fourth, fifth, and sixth authors was supported by the Prometeo/Generalitat Valenciana, Proyectos MTM2010-15296, MTM2010-19938-C03-02 Fundacio Bancaixa P11B2010-47 and Fondos Feder. The third author gratefully acknowledges financial support by ERC Advanced Grant 291512. The seventh author was supported by the NSA (grant H98230-13-1-0229). The eighth author gratefully acknowledges the support of the NSF (grants DMS-0901241 and DMS-1201374).
Article copyright: © Copyright 2015 American Mathematical Society