Czechoslovak Mathematical Journal, Vol. 69, No. 3, pp. 665-670, 2019
On the number of isomorphism classes of derived subgroups
Leyli Jafari Taghvasani, Soran Marzang, Mohammad Zarrin
Received October 7, 2017. Published online November 29, 2018.
Abstract: We show that a finite nonabelian characteristically simple group $G$ satisfies $n=|\pi(G)|+2$ if and only if $G\cong A_5$, where $n$ is the number of isomorphism classes of derived subgroups of $G$ and $\pi(G)$ is the set of prime divisors of the group $G$. Also, we give a negative answer to a question raised in M. Zarrin (2014).
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