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Arithmetical conditions of orbit sizes of linear groups of odd order

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Abstract

We study a conjecture of Gluck and a conjecture of Navarro for groups of odd order. We use some innovative techniques to obtain bounds beyond what is known.

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Acknowledgements

This work was partially supported by NSFC (No. 11671063), the Natural Science Foundation of Chongqing (cstc2016jcyjA0065, cstc2018jcyjAX0060), and a grant from the Simons Foundation (No. 499532). The author would also like to thank the referee for the valuable suggestions which greatly improved the paper.

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Authors and Affiliations

  1. Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX, 78666, USA

    Yong Yang

  2. Key Laboratory of Group and Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing, 402160, China

    Yong Yang

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  1. Yong Yang
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Correspondence to Yong Yang.

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Yang, Y. Arithmetical conditions of orbit sizes of linear groups of odd order. Isr. J. Math. 237, 1–14 (2020). https://doi.org/10.1007/s11856-020-1963-6

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  • DOI: https://doi.org/10.1007/s11856-020-1963-6

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