Skuratovskii, Ruslan V. On commutator subgroups of Sylow 2-subgroups of the alternating group, and the commutator width in wreath products. (English) Zbl 1507.20011 Eur. J. Math. 7, No. 1, 353-373 (2021). Summary: We find the size of a minimal generating set for the commutator subgroup of Sylow 2-subgroups of alternating group and investigate the structure of the commutator subgroup of Sylow 2-subgroups of the alternating group \(A_{2^k}\). This work continues previous investigations of the author [Cybern. Syst. Anal. 45, No. 1, 25–37 (2009; Zbl 1189.20007); translation from Kibern. Sist. Anal. 2009, No. 1, 27–41 (2009); ROMAI J. 13, No. 1, 117–139 (2017; Zbl 1424.20022)], where minimal generating sets of Sylow 2-subgroups of alternating groups were found. MSC: 20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure 20B35 Subgroups of symmetric groups 20E08 Groups acting on trees 20E22 Extensions, wreath products, and other compositions of groups 20F05 Generators, relations, and presentations of groups 20F12 Commutator calculus 20D06 Simple groups: alternating groups and groups of Lie type Keywords:commutator subgroup; alternating group; minimal generating set; Sylow 2-subgroups; Sylow \(p\)-subgroups; commutator width; permutational wreath product Citations:Zbl 1189.20007; Zbl 1424.20022 PDFBibTeX XMLCite \textit{R. V. Skuratovskii}, Eur. J. Math. 7, No. 1, 353--373 (2021; Zbl 1507.20011) Full Text: DOI References: [1] Bartholdi, L., Groth, T., Lysenok, I.: Commutator width in the first Grigorchuk group (2017). arXiv:1710.05706 [2] Bondarenko, IV; Samoilovych, IO, On finite generation of self-similar groups of finite type, Int. J. 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