Introduction A special monoid is a monoid presented by generators and defining relations of the form w = e, where w is a non-empty word on generators and e is the empty word. Groups are special monoids. But there exist special monoids that are not groups. Special monoids have been extensively studied by Adjanfl] and Makanin[7] (see also [2]). The present paper is a sequel to [11]. In [11], we s...

This paper is a continuation of paper [1] where we proved that for every linear finitely generated group G and any injective endomorphism φ of G, the mapping torus of φ is residually finite. The mapping torus of φ is the following ascending HNN extension of G: HNNφ (G) = 〈G, t | txt−1 = φ(x)〉 where x runs over a (finite) generating set of G. Probably, the most important mapping tori are mapping...

A group is called coherent when all of its finitely generated subgroups are finitely presented. Although many examples of coherent groups are known, (most notably polycyclic groups and 3-manifold groups) few tests are known for positively determining the coherence of an arbitrary group presentation. In this article we provide such a test. The test is based upon a definition of the perimeter of ...

| In this paper, we consider a matrix-algebraic approach to linear group-wise successive interference cancellation. As for both successive and parallel cancellation, it is shown that the general linear group-wise scheme corresponds to a one-shot linear matrix ltering. Furthermore , it is shown that if the general structure converges, it converges to the decorrelator. Four structures are conside...

Let $p$ be a prime. We produce two new families of pro-$p$ groups which are not realizable as absolute Galois fields. To prove this we use the 1-smoothness property groups. Moreover, show in these one has one-relator may ruled out employing quadraticity cohomology (a consequence Rost-Voevodsky Theorem), or vanishing Massey products cohomology.