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.