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Recognizing finite groups through order and degree patterns

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Abstract

The degree pattern of a finite group G associated with its prime graph has been introduced by Moghaddamfar in 2005 and it is proved that the following simple groups are uniquely determined by their order and degree patterns: All sporadic simple groups, the alternating groups A p (p ≥ 5 is a twin prime) and some simple groups of the Lie type. In this paper, the authors continue this investigation. In particular, the authors show that the symmetric groups S p+3, where p + 2 is a composite number and p + 4 is a prime and 97 < p ∈ π(1000!), are 3-fold OD-characterizable. The authors also show that the alternating groups A116 and A134 are OD-characterizable. It is worth mentioning that the latter not only generalizes the results by Hoseini in 2010 but also gives a positive answer to a conjecture by Moghaddamfar in 2009.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Yanxiong Yan, Guiyun Chen & Haijing Xu

  2. Department of Mathematics and Information Engineering, Chongqing University of Education, Chongqing, 400067, China

    Yanxiong Yan

  3. College of Mathematics Science, Chongqing Normal University, Chongqing, 401331, China

    Yanxiong Yan

  4. College of Mathematics and Statistics, Chongqing University, Shapingba, Chongqing, 401331, China

    Liangcai Zhang

Authors
  1. Yanxiong Yan
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  2. Guiyun Chen
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  3. Liangcai Zhang
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  4. Haijing Xu
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Corresponding author

Correspondence to Guiyun Chen.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11271301, 11171364), the National Science Foundation for Distinguished Young Scholars of China (No. 11001226), the Fundamental Research Funds for the Central Universities (Nos.XDJK2012D004, XDJK2009C074), the Natural Science Foundation Project of CQ CSTC (Nos. 2011jjA00020, 2010BB9206) and the Graduate-Innovation Funds of Science of Southwest University (No. ky2009013).

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Yan, Y., Chen, G., Zhang, L. et al. Recognizing finite groups through order and degree patterns. Chin. Ann. Math. Ser. B 34, 777–790 (2013). https://doi.org/10.1007/s11401-013-0787-7

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  • DOI: https://doi.org/10.1007/s11401-013-0787-7

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