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THE GROUP OF GRAPH AUTOMORPHISMS OVER A MATRIX RING

  • Park, Sang-Won (DEPARTMENT OF MATHEMATICS DONG-A UNIVERSITY) ;
  • Han, Jun-Cheol (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY)
  • Received : 2009.09.25
  • Published : 2011.03.01

Abstract

Let R = $Mat_2(F)$ be the ring of all 2 by 2 matrices over a finite field 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 $\Gamma(R)$ (the zero-divisor graph of R) is isomorphic to the symmetric group $S_{|F|+1}$ of degree |F|+1.

Acknowledgement

Supported by : Dong-A University

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