In this paper we study the capacity/entropy region of finite, directed,acyclic, multiple-sources, multiple-sinks network by means of group theory andentropy vectors coming from groups. There is a one-to-one correspondencebetween the entropy vector of a collection of n random variables and a certaingroup-characterizable vector obtained from a finite group and n of itssubgroups. We are looking at nilpotent group characterizable entropy vectorsand show that they are all also Abelian group characterizable, and hence theysatisfy the Ingleton inequality. It is known that not all entropic vectors canbe obtained from Abelian groups, so our result implies that in order to getmore exotic entropic vectors, one has to go at least to soluble groups orlarger nilpotency classes. The result also implies that Ingleton inequality issatisfied by nilpotent groups of bounded class, depending on the order of thegroup.
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