Study on Application of Lagrange’S Theorem In Cosets: Exploring the applications of Lagrange's Theorem in analyzing finite groups

Abstract

Lagrange's Theorem, one of the most important results infinite group theory, states that the order of a subgroup must divide the orderof the group. This theorem provides a powerful tool for analyzing finitegroups; it gives us an idea of exactly what type of subgroups we might expect afinite group to possess. Central to understanding Lagrange’s Theorem is thenotion of a coset.