We address the outstanding problem of electron pairing in presence strong Coulomb repulsion at small to moderate values parameter, ${r}_{s}\ensuremath{\lesssim}2$, and demonstrate that pseudopotential framework is fundamentally biased uncontrolled. Instead, one has break net result into two distinctively different effects: Fermi liquid renormalization factor change effective low-energy coupling...

We say that finite groups are isospectral if they have the same sets of orders elements. It is known every nonsolvable group $G$ to a simple has unique nonabelian composition factor, is, quotient by solvable radical an almost group. The main goal this paper prove cyclic extension its socle. To end, we consider general situation when arbitrary with not necessarily group, and study prime graph $G...