A General Framework for Learning Algebraic Properties from Cayley Graphs using Graph Neural Networks

A Graph Neural Network (GNN) framework for predicting the solvability of finite groups from their Cayley graph representations was introduced in [1]. In the present work, we generalize this approach and develop a property-independent framework for learning algebraic properties of finite groups directly from Cayley graphs. As representative case studies, we consider abelianity, nilpotency, and solvability. Using a common GNN architecture and training pipeline, we investigate the extent to which algebraic structure can be recovered from graph-based representations alone. Results on a collection of finite groups drawn from several families demonstrate that the framework successfully learns and distinguishes multiple algebraic properties from their associated Cayley graphs. These findings suggest that substantial algebraic information is encoded in graph representations and can be extracted through GNNs. More broadly, the proposed framework provides a proof of concept for applying graph representation learning to the study of algebraic properties of finite groups.