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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On large orbits of subgroups of linear groups


Authors: H. Meng, A. Ballester-Bolinches and R. Esteban-Romero
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 20C15, 20D20, 20D45
DOI: https://doi.org/10.1090/tran/7639
Published electronically: May 9, 2019
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Abstract: The main aim of this paper is to prove an orbit theorem and to apply it to obtain a result that can be regarded as a significant step towards the solution of Gluck's conjecture on large character degrees of finite solvable groups.


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Additional Information

H. Meng
Affiliation: Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, 46100 Burjassot, València, Spain
Email: hangyangmenges@gmail.com

A. Ballester-Bolinches
Affiliation: Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, 46100 Burjassot, València, Spain
Email: adolfo.ballester@uv.es

R. Esteban-Romero
Affiliation: Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, 46100 Burjassot, València, Spain
Address at time of publication: Permanent address: Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022 València, Spain
Email: ramon.esteban@uv.es, resteban@mat.upv.es

DOI: https://doi.org/10.1090/tran/7639
Keywords: Finite groups, solvable groups, linear groups, regular orbits, representations of groups
Received by editor(s): September 27, 2017
Received by editor(s) in revised form: June 4, 2018
Published electronically: May 9, 2019
Additional Notes: The research of this paper has been supported by the grant MTM2014-54707-C3-1-P from the Ministerio de Economía y Competitividad, Spain, and FEDER, European Union, and by the grant PROMETEO/2017/057 from the Generalitat, Valencian Community, Spain.
The first author was supported by the predoctoral grant 201606890006 from the China Scholarship Council.
Article copyright: © Copyright 2019 American Mathematical Society