发表机构
Ramat Gan Academic College（拉马特甘学术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对计算群论中判断有限群子群关系的基本问题，提出用连体图神经网络，结合有限群的凯莱图表示与代数特征来学习子群关系，实验证明此方法有效，在独立测试集上准确率达95.9% 。
AI 中文摘要
确定一个有限群是否同构于另一个有限群的子群是计算群论中的一个基本问题。在这项工作中，我们提出了一种连体图神经网络（Siamese GNN）用于子群预测，使用有限群的凯莱图表示。每个输入群由其无向凯莱图表示，并由连体GNN的一个分支编码以生成图嵌入。将得到的图嵌入与直接从输入群导出的代数特征相结合，构建联合特征向量，由全连接分类器处理以预测有限群之间的子群关系。通过整合基于图的结构表示和代数特征，该框架提供了一种从有限群学习子群关系的统一方法。实验结果证明了所提架构的有效性，在独立测试集上达到了95.9%（47/49）的测试准确率，说明了几何深度学习在子群预测方面的潜力。
英文摘要
Determining whether one finite group is isomorphic to a subgroup of another is a fundamental problem in computational group theory. In this work, we propose a Siamese Graph Neural Network (Siamese GNN) for subgroup prediction using Cayley graph representations of finite groups. Each input group is represented by its undirected Cayley graph and encoded by one branch of a Siamese GNN to produce a graph embedding. The resulting graph embeddings are combined with algebraic features derived directly from the input groups to construct a joint feature vector, which is processed by a fully connected classifier to predict subgroup relations between finite groups. By integrating graph-based structural representations with algebraic features, the proposed framework provides a unified approach for learning subgroup relations from finite groups. Experimental results on an expanded and more diverse dataset of 308 finite-group pairs drawn from 11 group families demonstrate the effectiveness of the proposed architecture, achieving a test BA of 91.67% on an independent test set. Additional experiments evaluate generalization to unseen groups, robustness to different Cayley graph generating sets, the contribution of GNN message passing, performance relative to non-neural baselines, and comparison with exact computational methods. These results illustrate the potential of geometric deep learning for subgroup prediction.
Journal refComputation 2026, 14, 204
DOI：10.3390/computation14090204
