Cosets and Lagrange's Theorem

Definition of Left Coset

Definition of Right Coset

Coset Representatives

Partitioning the Group

Equal Size of Cosets

Coset Equality Conditions

Definition and Calculation

Finite and Infinite Index

Statement and Proof

Geometric Interpretation

Order of an Element Divides Order of the Group

Groups of Prime Order are Cyclic

Subgroups of Prime Index

Fermat's Little Theorem

Euler's Theorem

Counting Arguments

Non-existence Results