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| Recognizing Finite Groups Through Order and Degree Patterns |
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Citation： |
Yanxiong YAN,Guiyun CHEN,Liangcai ZHANG,Haijing XU.Recognizing Finite Groups Through Order and Degree Patterns[J].Chinese Annals of Mathematics B,2013,34(5):777~790 |
| Page view： 1890
Net amount： 1495 |
Authors： |
Yanxiong YAN; Guiyun CHEN; Liangcai ZHANG; Haijing XU; |
Foundation： |
National Natural Science Foundation of China (Nos. 11271301, 11171364),the National Science Foundation for Distinguished Young Scholars of China (No. 11001226), the FundamentalResearch Funds for the Central Universities (Nos.XDJK2012D004, XDJK2009C074), theNatural 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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| 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 Ap (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 Sp+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. |
Keywords： |
Prime graph, Degree pattern, Degree of a vertex |
Classification： |
20D05, 20D10 |
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