Ahanjideh, N. (2019). Finite groups with the same conjugacy class sizes as a finite simple group. International Journal of Group Theory, 8(1), 23-33. doi: 10.22108/ijgt.2017.21236
Neda Ahanjideh. "Finite groups with the same conjugacy class sizes as a finite simple group". International Journal of Group Theory, 8, 1, 2019, 23-33. doi: 10.22108/ijgt.2017.21236
Ahanjideh, N. (2019). 'Finite groups with the same conjugacy class sizes as a finite simple group', International Journal of Group Theory, 8(1), pp. 23-33. doi: 10.22108/ijgt.2017.21236
Ahanjideh, N. Finite groups with the same conjugacy class sizes as a finite simple group. International Journal of Group Theory, 2019; 8(1): 23-33. doi: 10.22108/ijgt.2017.21236
Finite groups with the same conjugacy class sizes as a finite simple group
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 $S$, $G \cong S \times Z(G)$.
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