Open AccessA Constructive Method for Generating Short Presentations for the Symmetric Groups Sm+n, S2m and Smn
Author(s) -
D. Samaila,
G. N. Shu’aibu,
Babagana Modu
Publication year - 2021
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2021/v36i930400
Subject(s) - constructive , cartesian product , group (periodic table) , product (mathematics) , cartesian coordinate system , presentation (obstetrics) , mathematics , classical group , computer science , combinatorics , algebra over a field , pure mathematics , physics , geometry , programming language , process (computing) , lie group , medicine , radiology , quantum mechanics
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 the presentations of Sm and Sn. The aim is achieved by considering finite groups acting on sets and Cartesian product of groups which lead to the construction of multiple transformations as representatives of some finite groups.