What is Lagrange's theorem (group theory)?
'''Lagrange's theorem''' in [[group theory]] states if G is a finite [[group (mathematics)|group]] and H is a [[subgroup]] of G, then |H| (how many elements are in H, called the order of H) divides |G|. Moreover, the number of distinct left (right) [[coset]]s of H in G is |G|/|H|. This theorem is named after mathematician [[Joseph-Louis Lagrange]]. '''Applications''' * For any g in a group G, <math>g^k=e</math> for some k that divides the |G| * Any group of prime order cyclic (Any element in G can be created by a single element) and simple (no normal subgroups that aren't trivial) {{Math-stub}} [[Category:Group theory]] [[Category:Mathematical theorems]]