Abstract Algebra. Corollaries of Lagrange's Theorem

Title: Abstract Algebra. Corollaries of Lagrange's Theorem

Abstract: We describe several important corollaries of Lagrange's Theorem, which says that the size of a finite group is always divisible by the size of a subgroup. We use this to show that the order of any element in a group divides evenly into the order of the group, and that any group of prime size is a cyclic group. A further corollary is Fermat's Little Theorem.