Graph Neural Networks for Predicting Solvability of Finite Groups

arXiv cs.LG Papers
graph-neural-networks group-theory solvability-prediction machine-learning mathematics ai-for-math

Summary

This paper applies graph neural networks to predict the solvability of finite groups, demonstrating an AI-driven approach to a classic problem in group theory.

arXiv:2606.07619v1 Announce Type: new 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
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# Graph Neural Networks for Predicting Solvability of Finite Groups
Source: [https://arxiv.org/abs/2606.07619](https://arxiv.org/abs/2606.07619)
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