Automorphism group of rank-decreasing graph of matrices

Let F be a finite field, a positive integer, and the set consisting of all n × n matrices over F. The rank-decreasing graph of is a directed graph with vertex set , and there is a directed edge from to if and only if . In [Automorphism group of the rank-decreasing graph over the semigroup of upper t...

Full description

Saved in:
Bibliographic Details
Published in:Communications in algebra 2019-08, Vol.47 (8), p.3181-3189
Main Authors: Ou, Shikun, Wong, Dein
Format: Article
Language:English
Subjects:
Automorphism groups
Automorphisms
directed graphs
Fields (mathematics)
Graph theory
rank-decreasing graphs
zero-divisor graphs
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let F be a finite field, a positive integer, and the set consisting of all n × n matrices over F. The rank-decreasing graph of is a directed graph with vertex set , and there is a directed edge from to if and only if . In [Automorphism group of the rank-decreasing graph over the semigroup of upper triangular matrices, Comm. Algebra, 44(2016): 4088-4096], the authors described the automorphisms of the subgraph of induced by all upper triangular matrices in , and left the automorphisms of open. In this paper, we determine the automorphisms of .
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2018.1552287