Lagrange's theorem, in group theory, a part of mathematics, states that for any finite group G, the order of every subgroup of G divides the order of G. The theorem is named after Joseph-Louis Lagrange.

What is Lagrange theorem formula?

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.

Why is Lagrange's theorem important?

Lagrange's theorem is a statement in group theory which can be viewed as an extension of the number theoretical result of Euler's theorem. It is an important lemma for proving more complicated results in group theory.