Question

state and prove lagranges theorem on group

Answer 1

Step-by-step explanation:

Lagrange theorem states that the order of the subgroup H is the divisor of the order of the group G. If G is a group of finite order m, then the order of any a∈G divides the order of G and in particular am = e.

Proof of Lagrange Statement:

Let H be any subgroup of the order n of a finite group G of order m. Let us consider the cost breakdown of G related to H. Now let us consider each coset of aH comprises n different elements. Let H = {h1,h2,…,hn}, then ah1,ah2,…,ahn are the n distinct members of aH.