Abstract Algebra: Subgroups

Introduction (0:00)
Definition of subgroup (0:24)
Examples (4:24)
Facts about subgroups (11:00)
Subgroup criterion (11:36)
Subgroup criterion for finite sets (14:39)
Intersections of subgroups are subgroups (16:49)
Subgroups generated by subsets (19:02)
Finitely generated groups (20:56)
Example of a non-finitely generated group (25:08)
How to construct the subgroup generated by a set (28:43)
Orders of elements (31:32)
Order of an element equals order of subgroup it generates (36:25)
Lattices of subgroups (41:39)