THE GROUP OF GRAPH AUTOMORPHISMS OVER A MATRIX RING
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Let R = Mat_2(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 Γ(R) (the zero-divisor graph of R) is isomorphic to the symmetric group <수식> of degree <수식>.
Abstract
Let R = Mat_2(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 Γ(R) (the zero-divisor graph of R) is isomorphic to the symmetric group <수식> of degree <수식>.
참고문헌 (12)
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