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Large orbit sizes in finite group actions
Authors:Guohua Qian  Yong Yang
Institution:1. Dept. Mathematics, Changshu Institute of Technology, Changshu, Jiangsu, 215500, China;2. Dept. Mathematics, Texas State University, San Marcos, TX 78666, USA;3. Key Laboratory of Group and Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing, 402160, China;1. Mathematisches Institut, Justus-Liebig-Universität Gießen, Germany;2. Graduate School of Information Science and Technology, The University of Tokyo, Japan;3. Cyber Physical Security Research Center, National Institute of Advanced Industrial Science and Technology, Japan;1. Department of Mathematics, University of Auckland, Auckland, New Zealand;2. Department of Mathematics and National Center for Theoretical Sciences (South), National Cheng Kung University, Taiwan
Abstract:In this paper, we study the relations of the sizes of various sections of finite linear groups and the largest orbit size of the linear group actions. We also study various applications of those orbit theorems.
Keywords:Keywords Finite group  Group action  Orbit size
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