On $p$-Central Automorphisms of Primitive Groups and Applications
Received:February 27, 2018  Revised:May 16, 2018
Key Word: $p$-central automorphism   Coleman automorphism   the normalizer conjecture  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.71571108), Projects of International (Regional) Cooperation and Exchanges of NSFC (Grant Nos.71611530712; 61661136002), Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20133706110002), Natural Science Foundation of Shandong Province (Grant No.ZR2015GZ007), Project Funded by China Postdoctoral Science Foundation (Grant No.2016M590613) and the Specialized Fund for the Postdoctoral Innovative Research Program of Shandong Province (Grant No.201602035).
Author NameAffiliation
Shenjuan DONG School of Mathematics and Statistics, Qingdao University, Shandong 266071, P. R. China
Institute of Applied Mathematics of Shandong, Shandong 266071, P. R. China 
Zhengxing LI School of Mathematics and Statistics, Qingdao University, Shandong 266071, P. R. China
Institute of Applied Mathematics of Shandong, Shandong 266071, P. R. China 
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Abstract:
      Let $G$ be a primitive group. It is proved that there exits some prime $p$ such that every $p$-central automorphism of $G$ is inner. As an application, it is proved that every Coleman automorphism of the holomorph of $G$ is inner. In particular, the normalizer property holds for such groups in question. Additionally, other related results are obtained as well.
Citation:
DOI:10.3770/j.issn:2095-2651.2019.01.003
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