Herzog, Marcel; Longobardi, Patrizia; Maj, Mercede On the number of commutators in groups. (English) Zbl 1122.20017 Arad, Zvi (ed.) et al., Ischia group theory 2004. Proceedings of a conference in honor of Marcel Herzog, Naples, Italy, March 31–April 03, 2004. Providence, RI: American Mathematical Society (AMS); Ramat Gan: Bar-Ilan University (ISBN 0-8218-3711-7/pbk). Contemporary Mathematics 402. Israel Mathematical Conference Proceedings, 181-192 (2006). This interesting article is dedicated to the groups with a finite set of subgroups serving as commutator subgroups of some subgroups of the group (C-groups). The authors obtain a general description of C-groups and some details of the structure of perfect C-groups with no proper subgroups of finite index. Among others, they prove that a C-group has finitely generated commutator subgroup. The authors also describe the groups in which every non-Abelian subgroup has the commutator subgroup coinciding with the commutator subgroup of the whole group. In particular, they prove that such a group is solvable if and only if it is locally graded.For the entire collection see [Zbl 1089.20500]. Reviewer: Igor Subbotin (Los Angeles) Cited in 1 ReviewCited in 8 Documents MSC: 20F14 Derived series, central series, and generalizations for groups 20E34 General structure theorems for groups 20F16 Solvable groups, supersolvable groups 20E25 Local properties of groups 20E07 Subgroup theorems; subgroup growth Keywords:commutator subgroups; locally graded groups; perfect groups; subgroups of finite index; non-Abelian subgroups; solvable groups PDFBibTeX XMLCite \textit{M. Herzog} et al., Contemp. Math. 402, 181--192 (2006; Zbl 1122.20017)