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On the number of isomorphism classes of derived subgroups

Leyli Jafari Taghvasani; Soran Marzang; Mohammad Zarrin — 2019

Czechoslovak Mathematical Journal

We show that a finite nonabelian characteristically simple group $G$ satisfies $n = | π (G) | + 2$ if and only if $G ≅ A_{5}$ , where $n$ is the number of isomorphism classes of derived subgroups of $G$ and $π (G)$ 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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