# Groups Lecture 14

in which we meet several standard actions and prove Cayley’s Theorem.

# Groups Lecture 10

in which we apply group theory to prove Fermat-Euler, use Lagrange to help us find subgroups or determine what a small group must look like, and meet normal subgroups.

# Groups Lecture 9

in which apply Lagrange’s Theorem to prime order groups, meet equivalence relations and further explore multiplication modulo n.

# Groups Lecture 8

in which we show that the sign of a permutation is a surjective group homomorphism, meet cosets and prove Lagrange’s Theorem.

# Groups Lecture 14

in which we meet orbits and stabilisers and prove the Orbit-Stabiliser Theorem.

# Groups Lecture 10

in which we apply group theory to prove Fermat-Euler, and use Lagrange to help us find subgroups or determine what a small group must look like.

# Groups Lecture 9

in which we finish the proof of Lagrange’s Theorem, see what consequences it has on orders of elements, and meet equivalence relations.