University of Isfahan International Journal of Group Theory 2251-7650 8 1 2019 03 01 Finite groups with the same conjugacy class sizes as a finite simple group 23 33 21236 10.22108/ijgt.2017.21236 EN Neda Ahanjideh University of Shahre-kord Journal Article 2016 05 01 For a finite group $H$‎, ‎let $cs(H)$ denote the set of non-trivial conjugacy class sizes of $H$ and $OC(H)$ be the set of the order components of $H$‎. ‎In this paper‎, ‎we show that if $S$ is a finite simple group with the disconnected prime graph and $G$ is a finite group such that $cs(S)=cs(G)$‎, ‎then $|S|=|G/Z(G)|$ and $OC(S)=OC(G/Z(G))$‎. ‎In particular‎, ‎we show that for some finite simple group $S$‎, ‎$G \cong S \times Z(G)$‎. https://ijgt.ui.ac.ir/article_21236_1a260ed6b265defd6362bf30cf33c9ce.pdf