兼容近環是環的一種推廣，其結構自然地源自群的內自同構。 對 任意群G，記I(G)為G的所有有限個內自同構之和所構成的集合。 內 自同構近環I(G)的概念在近環理論中扮演著主導性的角色，我們知道 這類近環是具有兼容性的。 在本文中，我們將研究某一類特定的兼 容近環I(G)及其良好的代數性質。
當I(G)構成一個環時，稱G為一個I-群，這一類環I(G)的刻畫介於 群論與近環論的接縫處。 在本文中，當G為有3^6階的I-群時，我們將 對其環I(G)的結構進行刻畫， 對於這類自然的交換環I(G)，我們考慮 其零因子圖Γ(I(G))及其對應的鄰接矩陣A(Γ(I(G)))。

Compatible nearrings are a generalization of rings with identity that arise naturally from inner automorphisms of groups. For any group G, let I(G) denote the set of all finite sums of inner automorphisms of G. The concept of inner automorphism nearrings I(G) plays a dominant role in nearring theory. It is known that nearrings I(G) are compatible. In this article, a certain class of such compatible nearrings I(G) and their good properties will be discussed.
When I(G) forms a ring, G is referred to as an I-group. The characteriza- tion of the ring I(G) for an I-group G is at the seam between nearring theory and group theory. In this article, the ring structure of I(G) will be determined when G is an I-group with |G| = 3^6. For such natural commutative rings I(G), we consider their zero divisor graphs Γ(I(G)) and the corresponding adjacency matrices A(Γ(I(G))).

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