A long-standing problem is how to create a short-length presentation for finite groups of degree n. This paper aimed at presenting a concrete method for generating presentations for the groups Sm+n, S2m and Smn for all m,nÎZ+ with fewer relations than the existing literature from...
Open access
Research Article10.9734/jamcs/2021/v36i930400
The use of finite group presentations in signal processing has not been exploit in the current literature. Based on the existing signal processing algorithms (not necessarily group theoretic approach), various signal processing transforms have unique decomposition capabilities, t...
Open access
Research Article10.9734/jamcs/2021/v36i930398
Our goal in this paper is to generate functions fi from a finite group G to itself such that each fi’s are morphisms. The concept of the fundamental theorem of finite Abelian group was introduced and we proved the result that if G is any finite Abelian group, then the factor grou...
Open access
Research Article10.9734/JSRR/2016/26346
In this paper, we present some methods of constructing new groups from given ones. We first examined the direct product of the finite groups Gi for n³2 and then observed that . We also established the fact that for any prime number p > 2 and any positive integer k, |U(pk)| =...
Open access
Research Article10.9734/JSRR/2016/26080
The main objective of this paper is to determine the non-Abelian finite groups which contain only Abelian and Hamiltonian subgroups and to obtain some of their fundamental properties. Two exceptional groups of orders 16 and 24 were examined and are completely determined using GAP...
Based on the concept of group representation theory, new representations can be generated by direct product (or tensor product) of any two representations of a group. In such case, their irreducible representations are also the direct product. But the conditions under which these...
Open access
Research Article10.9734/ARJOM/2018/43157
The symmetric genus of a finite group G is defined as the smallest genus s of a compact connected oriented surface on which G acts faithfully via diffeomorphisms, which may be orientation-preserving or orientation-reserving. In this paper we determine a useful lower bound for the...
Open access
Research Article10.9734/ARJOM/2017/36239