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  • GUOHUA QIAN (a1) and YONG YANG (a2) (a3)


For every element $x$ of a finite group $G$ , there always exists a unique minimal subnormal subgroup, say, $G_{x}$ of $G$ such that $x\in G_{x}$ . The sub-class of $G$ in which $x$ lies is defined by $\{x^{g}\mid g\in G_{x}\}$ . The aim of this paper is to investigate the influence of the sub-class sizes on the structure of finite groups.


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This project was supported by the NSF of China (nos. 11471054, 11671063, and 11871011), the NSF of Jiangsu Province (no. BK20161265), the Natural Science Foundation of Chongqing (cstc2016jcyjA0065, cstc2018jcyjAX0060), and a grant from the Simons Foundation (no. 499532).



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