Geodesic
On the number of isomorphism classes of derived subgroups
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 665-670
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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).
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).
DOI : 10.21136/CMJ.2018.0464-17
Classification : 20F24
Keywords: derived subgroup; simple group 
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Taghvasani, Leyli Jafari; Marzang, Soran; Zarrin, Mohammad. On the number of isomorphism classes of derived subgroups. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 665-670. doi: 10.21136/CMJ.2018.0464-17

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