We give another expression of the longest elements of classical coxeter groups , the action of the longest element of the finite reflection group on the simple system and a special automorphism of finite reflection groups corresponding to the longest elements.

Directed subgroup graph for studying the subgroup properties of finite groups;

On the solvability of finite groups based on normal indexes;

A new graph of conjugacy classes of finite groups;

The number of the orders of non-normal subgroups and the structure of finite groups;

s-normality subgroups of finite groups and solvablity;