Non-Jordaness of the automorphism group of the zero-divisor graph of a matrix ring over number rings
Abstract
We provide a construction of the induced subgraphs of the zero-divisor graph of M2(R) for the ring R of algebraic integers of some number fields that are neither complete nor connected, and study the structure of the induced subgraphs explicitly. As an application, we prove that the automorphism group of the zero-divisor graph of M2(R) is not a Jordan group.
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