On commutator subgroups of Sylow 2-subgroups of the alternating group, and the commutator width in wreath products

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(2k). This work continues previous investigations of the author (Skuratovskii in Cybern Syst Anal 45(1):25-37, 2009; ROMAI J 13(1):117-139, 2017), where minimal generating sets of Sylow 2-subgroups of alternating groups were found.