In this paper we give necessary and sufficient conditions for the efficiency of the semi-direct product of free abelian monoid with rank n by the infinite cyclic monoid.

Let us define A = [a(ij)](i,j=0)(n-1) and B = [b(ij)](i,j=0)(n-1) as n x n Toeplitz and Hankel matrices, respectively, such that a(ij) = Pi-j and b(ij) = Pi+j, where P denotes the Pell number. We present upper and lower ...

In this paper the Estrada index of Hermite matrix is firstly defined and investigated. In fact this is a natural generalization of Estrada, distance Estrada and Laplacian Estrada indices. Thus all properties about them can ...

The main purpose of this paper is to present a new example of deficiency one groups by considering the split extension of a finite cyclic group by a free abelian group having rank two.

In this paper we give necessary and sufficient conditions for the efficiency of a standard presentation for the semi-direct product of finite cyclic monoids by one-relator monoids.

In this work, subgroups of a special class of discrete subgroups of PLS(2, R), namely the ones of the first kind with genus 0, have been studied. We establish a technique to compute the genus of these subgroups in terms ...

At the present paper we show that conjugacy is preserved and reflected by the natural homomorphism defined from a semigroup S to a group G, where G defines split extensions of some free groups. The main idea in the proofs ...