In this paper, we find a combinatorial identity which is related to the multi-dimensional integral γ m in study of divisor functions (see (1)). As an application, determine finite dual group algebra infinite dihedral group.

Classic convolutional codes are defined as the convolution of a message and a transfer function over Z. In this paper, we study convolutional codes over the infinite dihedral group D∞. The goal of this study is to design convolutional codes with good and interesting properties and intended to be more resistant to code recognition. Convolution of two functions on D∞ corresponds to the product of...

This research is about the group coverings of subsets finite non-abelian groups and its application in field cryptography. Group abelian has been researched over years it many applications various fields. The popularity internet increased rapidly cryptography become more important as ensures privacy security users network. A cryptosystem a structure consisting several cryptographic primitives. ...

in this paper we define s algebras and show that every finite group can be found in some s algebra.  we define and study the s degree of a finite group and determine the s degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $d_p$.

Assuming that G is a finite group and H subgroup of G, the graph known as relative coprime with respect to (denoted Γ_(G,H)) has vertices corresponding elements G. Two distinct x y are adjacent by an edge if only (|x|,|y|)=1 or belongs H. This paper will focus on finding general formula for some topological indices dihedral group. The study in theory offers valuable insights into structural pro...

Let n be a natural number larger than two. Let D2n = ⟨r, s ∶ r = s = e, srs = r⟩ be the Dihedral group, and κ an n-dimensional unitary representation of D2n acting in C as follows. (κ(r)v)(j) = v((j−1) mod n) and (κ(s)v)(j) = v((n − j) mod n) for v = (v0,⋯, vn−1) ∈ C. For any representation which is unitarily equivalent to κ, we prove that when n is prime there exists a Zariski open subset E of...

In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if R is generalised dihedral group and CI-group, then for every odd prime p Sylow p-subgroup has order p, or 9. Consequently, any CI-group with quotient same restriction, that