Graph Neural Networks for Predicting Solvability of Finite Groups

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