On the number of isomorphism classes of derived subgroups
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We show that a finite nonabelian characteristically simple group G satisfies n = |π(G)| + 2 if and only if G ≅ A5, 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).
Keywordsderived subgroup simple group
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- The GAP Group: GAP-Groups, Algorithms, Programming-a System for Computa-tional Discrete Algebra, Version 4. 4. 2005; Available at http://www. gap-system. org. swGoogle Scholar
- B. Huppert: Finite Groups I. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 134, Springer, Berlin, 1967. (In German.)Google Scholar
- W. Shi: On simple K4-groups. Chin. Sci. Bull. 36 (1991), 1281–1283.Google Scholar
- M. Zarrin: On groups with finitely many derived subgroups. J. Algebra Appl. 13 (2014), Article ID 1450045, 5 pages.Google Scholar