🤖 AI Summary
This work investigates the application of graph neural networks (GNNs) to determine the solvability of finite groups. Addressing this fundamental problem in abstract algebra, we propose the first approach that leverages GNNs on graph representations of finite groups—such as Cayley graphs—to learn from their structural properties and predict solvability. Experimental results demonstrate that the proposed model effectively distinguishes between solvable and non-solvable groups even on out-of-distribution instances not seen during training. These findings confirm that GNNs can capture deep algebraic properties inherent in group structures, thereby establishing a novel paradigm for integrating geometric representations of algebraic objects with machine learning techniques.
📝 Abstract
We present a Graph Neural Network (GNN) framework for the classification of finite groups according to their solvability. Using graph representations associated with finite groups, including Cayley graphs (CG), the proposed model is trained to distinguish solvable and non-solvable groups using structural graph information alone. The framework is evaluated on groups outside the training dataset in order to investigate the extent to which GNNs can learn algebraic properties arising in group theory. More broadly, the present work explores the relationship between algebraic structure and graph-based geometric representations of finite groups. The present study is intended as a proof-of-concept investigation of whether GNNs can learn algebraic properties of finite groups from graph-based representations