A Constructive Method for Generating Short Presentations for the Symmetric Groups Sm+n, S2m and Smn

Samaila, D. and Shu’aibu, G. N. and Modu, B. A. (2021) A Constructive Method for Generating Short Presentations for the Symmetric Groups Sm+n, S2m and Smn. Journal of Advances in Mathematics and Computer Science, 36 (9). pp. 37-47. ISSN 2456-9968

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Official URL: https://doi.org/10.9734/jamcs/2021/v36i930400

Abstract

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.

Item Type:	Article
Subjects:	Science Repository > Mathematical Science
Depositing User:	Managing Editor
Date Deposited:	04 Apr 2023 04:41
Last Modified:	12 Mar 2024 03:59
URI:	http://research.manuscritpub.com/id/eprint/1731

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