On Connections between Group Homomorphisms and the Ingleton Inequality

In this paper, we show that random variables mapped under group homomorphisms from a uniformly distributed background random variable satisfy the Ingleton inequality. As corollaries, we recover two previous known results. The first is that the network throughput of linear network codes is, in general, constrained by the Ingleton inequality. The second and related result is that the network throughput of Abelian-group network codes - group network codes that are restricted to Abelian groups - is also constrained by the Ingleton inequality.