‎let $h$ be a prefrattini subgroup of a soluble finite group $g$‎. ‎in the‎ ‎paper it is proved that there exist elements $x,y in g$ such that the equality‎ ‎$h cap h^x cap h^y = phi (g)$ holds‎.

Introduction: The most common type of velopharyngeal valve (VPV) closure is a matter of controversy.The aim of this study was to estimate the most common type of VPV closure, including identification of the type and grade of VPV closure among Egyptian children.  Materials and Methods: This study included patients who were candidates for adenotonsillectomy. In these cases, video-nasoendoscopy an...

In this work we study Leibniz algebras whose second-maximal subalgebras are ideals. We provide classification based on solvability, nilpotency, and properties of the Frattini subalgebra. give several specific descriptions with these include necessary sufficient conditions for non-nilpotent case.