Symmetric Presentations of Finite Groups

Abstract

In abstract algebra, a symmetric group defined over a set is the group for which the composition of functions is the group operation, and whose members are all the bijections from the set to itself. Galois theory, invariant theory, lie group representation theory, and combinatorics are just a few of the many branches of mathematics that rely on the symmetric group. The mathematical field of group representation theory studies the effects that groups have on predetermined structures. Particular attention is paid here to group operations on vector spaces. Yet, we also take into account groups that operate upon other groups or sets. The primary goal of this study is to offer an alternate approach of describing group elements of finite simple groups that is both brief and informative. In this research, we show how we found some new symmetric constructions for significant finite groups. As the orders of our photographs are becoming more and bigger, we've started using Magma to help us out with some of the math.