一类完全 0 简单半群的幂图

Pub Date : 2024-02-26 DOI:10.1007/s10801-024-01306-1

Yanliang Cheng, Yong Shao, Lingli Zeng

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引用次数: 0

摘要

我们首先确定了完全 0 简单半群的幂图结构，然后给出了它们的幂图的一些性质。作为本文的主要结果，我们利用卡梅隆和戈什关于无边际群幂图的定理，得到了两个具有无边际群（\(\mathcal {H}\）类的 \(G^{0}\)-normal 完全 0-simple 正交半群 S 和 T 基于它们的幂图是同构的。我们还提出了一种判定 S 和 T 是否同构的算法。

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Power graphs of a class of completely 0-simple semigroups

We first determine the structure of the power digraphs of completely 0-simple semigroups, and then some properties of their power graphs are given. As the main result in this paper, using Cameron and Ghosh’s theorem about power graphs of abelian groups, we obtain a characterization that two \(G^{0}\)-normal completely 0-simple orthodox semigroups S and T with abelian group \(\mathcal {H}\)-classes are isomorphic based on their power graphs. We also present an algorithm to determine that S and T are isomorphic or not.

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