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Abstract
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.
Acknowledgements
The author would like to express his sincere gratitude to the referee for a very careful reading of the paper and for all his or her insightful comments and valuable suggestions, which make a number of improvements on this paper.
Notes
No potential conflict of interest was reported by the author.