We prove that if a group generated by a bireversible Mealy automaton contains an element of infinite order, its growth blows up and is necessarily exponential. As a direct consequence, no infinite virtually nilpotent group can be generated by a bireversible Mealy automaton. The study on how (semi)groups grow has been highlighted since Milnor’s question on the existence of groups of intermediate...

Transitive closures of the covering relation in semilattices are investigated. Vyšetřuj́ı se tranzitivńı uzávěry pokrývaćı relace v polosvazech. This very short note is an immediate continuation of [1]. We therefore refer to [1] as for terminology, notation, various remarks, further references, etc. 1. The covering relation in semilattices Throughout the note, let S = S(+) be a semilattice (i. e...

Wave propagation problems play an important role, not only in the scientific community, but also in industry. Think of acoustic scattering, sound radiation and other related problems. A common feature of these problems is the large or even infinite extension of the acoustic domain compared to the rather limited extension of the surface of the embedded scatterer. The appropriateness of solving s...

in this paper we consider the group algebra $r(c_2times‎ ‎d_infty)$‎. ‎it is shown that $r(c_2times d_infty)$ can be‎ ‎represented by a $4times 4$ block circulant matrix‎. ‎it is also‎ ‎shown that $mathcal{u}(mathbb{z}_2(c_2times d_infty))$ is‎ ‎infinitely generated‎.

Let (A,1) be a partially ordered set. The relation a 1 b can be read as “a precedes b”. For elements a and b in A, we write a ≺ b if and only if a 1 b and a 6= b holds. For notational convenience, we also write a o b if and only if a 1 b holds, and a  b if and only if a ≺ b holds. We call (A,1) a well-founded set if and only if every non-empty subset M of A contains at least one minimal elemen...

In this paper, a series of analysis with finite element method was carried out varying hole shapes perforation as well plate dimensions. Eight different models about holes that number edges at the is four to infinite namely circular presented. Than analyze results these boundary conditions fixed supported and simply were compared. study it has shown when for infinite, in other words circular, m...

groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.