Products of $\scr N$-connected groups

Abstract

Two subgroups $H$ and $K$ of a finite group $G$ are said to be $\mathcal N$-connected if the subgroup generated by $x$ and $y$ is a nilpotent group, for every pair of elements $x$ in $H$ and $y$ in $K$. This paper is devoted to the study of pairwise $\mathcal N$-connected and permutable products of finitely many groups, in the framework of formation and Fitting class theory.