Automorphisms of the subgroup-relation graph over the group of unit upper triangular matrices
Long Wang · Linear and Multilinear Algebra · 2015
Let be a finite field of odd characteristic, be a positive integer, be the group of all invertible upper triangular matrices over and be the derived subgroup of consisting of all unit upper triangular matrices. For , the normal subgroup of generated by , i.e. the minimum normal subgroup of containing , is denoted by . By , we denote the directed graph with vertex set , there is a directed edge from a vertex to a vertex if and only if the normal subgroup of generated by is properly contained in that of , i.e. . In this article, the normal subgroups of contained in are described, the graph automorphisms of are characterized.