Integrals of groups. II (Q6635127)

An integral of a group \(G\) is a group \(H\) whose derived group is isomorphic to \(G\). This paper continues the investigation on integrals of groups that the authors started earlier [the first author et al., Isr. J. Math. 234, No. 1, 149--178 (2019; Zbl 1458.20029)]. The authors study: \N\begin{itemize}\N\item a sufficient condition for a bound on the order of an integral for a finite integrable group and a necessary condition for a group to be integrable; \N\item the existence of integrals that are \(p\)-groups for abelian \(p\)-groups and of nilpotent integrals for all abelian groups; \N\item the variety of integrals of groups from a given variety;\N\item integrals of profinite groups. \N\item integrals of Cartesian products. \end{itemize}\NThey end the paper with a number of open problems.