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

In this work, we present a general Graph Neural Network (GNN) framework for learning algebraic properties of finite groups from their Cayley graph representations. The framework provides a unified computational pipeline consisting of a common graph construction procedure, feature representation, training methodology, and GNN architecture, with only the target labeling function varying across classification tasks. To demonstrate the generality of the proposed approach, we consider three representative algebraic properties: abelianity, nilpotency, and solvability. Experiments were conducted on a benchmark of 176 finite groups drawn from several classical families, with all groups included i...

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