GNNs trained on finite Cayley graphs generalize to truncated graphs of infinite groups including free abelian, Heisenberg, dihedral, and free groups.
Graph Neural Networks for Predicting Solvability of Finite Groups
2 Pith papers cite this work. Polarity classification is still indexing.
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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
years
2026 2representative citing papers
A GNN pipeline predicts abelianity, nilpotency, and solvability from Cayley graphs, with held-out PSL(2,q) groups classified correctly, though abstract and body report different accuracies.
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From Finite Cayley Graphs to Growth of Infinite Groups
GNNs trained on finite Cayley graphs generalize to truncated graphs of infinite groups including free abelian, Heisenberg, dihedral, and free groups.
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A General Framework for Learning Algebraic Properties from Cayley Graphs using Graph Neural Networks
A GNN pipeline predicts abelianity, nilpotency, and solvability from Cayley graphs, with held-out PSL(2,q) groups classified correctly, though abstract and body report different accuracies.