In the present work, we give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Moreover, we investigate the profinite topology of F 2 × F 2 and we show that the profinite topology of the above group is strongly connected with the profinite topology of F 2 .

The main usage of supermodular functions is to cross out tight sets, that is to use only the following important property. The intersection and the union of two sets with a maximal function value also have maximal function value. But for this purpose we do not need the full strength of supermodularity, some weaker concept suffices. We introduce here a new property, the so called λsupermodularit...

In this paper we introduce the smallest equivalence relation ξ∗ on a finite fuzzy hypergroup S such that the quotient group S/ξ∗, the set of all equivalence classes, is a solvable group. The characterization of solvable groups via strongly regular relation is investigated and several results on the topic are presented.

New (96,20,4,4) and (96,19,2,4) regular partial difference sets are constructed, together with the corresponding strongly regular graphs. Our source are (96,20,4) regular symmetric designs.

We examine the problem of finite-state representability of infinitestate processes w.r.t. certain behavioural equivalences. We show that the classical notion of regularity becomes insufficient in case of all equivalences of van Glabbeek’s hierarchy except bisimilarity, and we design and justify a generalization in the form of strong regularity and finite characterizations. We show that the cond...