THE GROUP OF GRAPH AUTOMORPHISMS OVER A MATRIX RING
THE GROUP OF GRAPH AUTOMORPHISMS OVER A MATRIX RING
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DOI：
10.4134/jkms.2011.48.2.301
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发表时间：
2011-03
影响因子：
4.5
通讯作者：
Sangwon Park;Juncheol Han
中科院分区：
文献类型：
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作者：
Sangwon Park;Juncheol Han
设R = Mat2（F）是有限域F上所有2 × 2矩阵组成的环，X是R的所有非零非单位元的集合，G是R的所有单位元的群.在研究了G在X上的左（右）正则作用下的轨道的一些性质后，证明了（R）（R的零因子图）的图自同构群同构于jFj +1次对称群SjFj +1.
Let R = Mat2(F) be the ring of all 2 by 2 matrices over a nite eld F, X the set of all nonzero, nonunits of R and G the group of all units of R. After investigating some properties of orbits under the left (and right) regular action on X by G, we show that the graph automorphisms group of ( R) (the zero-divisor graph of R) is isomorphic to the symmetric group Sj F j +1 of degree jFj + 1.