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The Ingleton inequality holds for metacyclic groups and fails for supersoluble groups
David A. Craven
https://arxiv.org/abs/2505.22565 https://

The Ingleton inequality holds for metacyclic groups and fails for supersoluble groups
The Ingleton inequality first appeared in matroid theory, where Ingleton proved in 1971 that every rank function coming from a representable matroid on four subsets satisfies a particular inequality. Because this inequality is not implied by submodularity, Shannon-type axioms alone, it and various analogues play a central role in separately linear and non-linear phenomena in a variety of areas of mathematics. The Ingleton inequality for finite groups concerns the various intersections of four s…