‎given a finite non-cyclic group $g$‎, ‎call $sigma(g)$ the smallest number of proper subgroups of $g$ needed to cover $g$‎. ‎lucchini and detomi conjectured that if a nonabelian group $g$ is such that $sigma(g) < sigma(g/n)$ for every non-trivial normal subgroup $n$ of $g$ then $g$ is textit{monolithic}‎, ‎meaning that it admits a unique minimal normal subgroup‎. ‎in this paper we show how thi...

Abstract Filamentary structures are recognized as a fundamental component of interstellar molecular clouds in observations made by the Herschel satellite. These filaments, especially massive often extend direction perpendicular to magnetic field. Furthermore, filaments sometimes have an apparently negative temperature gradient—that is, their temperatures decrease toward centers. In this paper, ...