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Characterization of PGL(2, p) by its order and one conjugacy class size

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Abstract

Let p be a prime. In this paper, we do not use the classification theorem of finite simple groups and prove that the projective general linear group P G L(2, p) can be uniquely determined by its order and one special conjugacy class size. Further, the validity of a conjecture of J. G. Thompson is generalized to the group P G L(2, p) by a new way.

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Acknowledgement

The authors would like to thank Professor G. H. Qian for his help in the proof of Lemma 2.3, and would also thank the reviewers for their kindness and valuable suggestions. This work was supported by National Natural Science Foundation of China (Grant Nos.11271301, 11426053), the Scientific Research Foundation of Chongqing Municipal Science and Technology Commission (Grant No. cstc2014jcyjA00009), the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJ1401006), the Foundation of Chongqing Three Gorges University (Grant No. 14ZD16).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    YANHENG CHEN & GUIYUN CHEN

  2. School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, People’s Republic of China

    YANHENG CHEN

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  1. YANHENG CHEN
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  2. GUIYUN CHEN
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Correspondence to GUIYUN CHEN.

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Communicating Editor: Parameswaran Sankaran

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CHEN, Y., CHEN, G. Characterization of PGL(2, p) by its order and one conjugacy class size. Proc Math Sci 125, 501–506 (2015). https://doi.org/10.1007/s12044-015-0253-4

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  • DOI: https://doi.org/10.1007/s12044-015-0253-4

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