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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)].
##### MSC:
 20F24 FC-groups and their generalizations
##### Keywords:
derived subgroup; simple group
GAP
Full Text:
##### References:
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