Group Theory · Algebra
Subgroups, Cosets, and Lagrange’s Theorem
Lagrange’s theorem partitions G into equal-sized cosets of H. As a corollary, the order of any element divides the order of the group.
WHAT STUDENTS WILL LEARN
✓Identify subgroups using the subgroup criterion
✓Construct left and right cosets
✓Prove Lagrange’s Theorem: |H| divides |G|
✓Apply to classify possible subgroup orders
BUILDS ON
COURSE OUTLINE · CLICK A PART FOR RESOURCES