AG25 Lagrange's Theorem for Finite Groups

3:13 Lagrange's Theorem: The size of a subgroup divides the order of the group. Corollaries: (1) 4:24 The order of an element of a group divides the order of a group; (2) 9:07 If p is a prime, a group of order p is cyclic and isomorphic to Z/pZ; (3) 12:56 A group of order 1081 is either abelian or the only element in its center is the identity; (4) 20:40 If H is a subgroup of K and K a subgroup of G then |G:H| is the product of |G:K| and |K:H|; (5) 24:52 The index of the center of a group is never a prime number.

A series of lectures for a full course on undergraduate abstract algebra based on my book:

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA, USA.