Abstract
It is a well-known fact that characters of a finite group can give important information about the structure of the group. It was also proved by the third author that a finite simple group can be uniquely determined by its character table. Here the authors attempt to investigate how to characterize a finite almost-simple group by using less information of its character table, and successfully characterize the automorphism groups of Mathieu groups by their orders and at most two irreducible character degrees of their character tables.
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This work was supported by the National Natural Science Foundation of China (Nos. 11426182, 11401324, 11271301, 11471266, 10871032), SRF for ROCS, SEM, the Fundamental Research Funds for the Central Universities (No. SWU115052), the Natural Science Foundation Project of CQ CSTC (Nos. cstc2014jcyjA00010, cstc2014jcyA0148, 2010BB9206) and the National Science Foundation for Distinguished Young Scholars of China (No. 11001226).
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Yan, Y., Zhang, L., Xu, H. et al. Recognizing the automorphism groups of Mathieu groups through their orders and large degrees of their irreducible characters. Chin. Ann. Math. Ser. B 37, 495–502 (2016). https://doi.org/10.1007/s11401-016-1024-y
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DOI: https://doi.org/10.1007/s11401-016-1024-y