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On the number of isomorphism classes of derived subgroups. (English) Zbl 07088811
Summary: 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 [J. Algebra Appl. 13, No. 7, Article ID 1450045, 5 p. (2014; Zbl 1303.20044)].
20F24 FC-groups and their generalizations
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