# Groups Lecture 18

in which we meet the quaternions, start exploring matrix groups and act with matrices on vectors and on matrices.

# Groups Lecture 17

in which we explore conjugacy classes in $S_n$ and $A_n$, and prove that $A_5$ is simple.

# Groups Lecture 12

in which we prove the Isomorphism Theorem and first meet group actions.

# Groups Lecture 11

in which we explore groups of order 6 and make a start on quotients.

# 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 18

in which we meet the quaternions and start exploring matrix groups.

# Groups Lecture 17

in which we explore conjugacy classes in $S_n$ and $A_n$, and prove that $A_5$ is simple.

# Groups Lecture 16

in which we prove Cauchy’s theorem and revisit the symmetric groups.

# Groups Lecture 12

in which we find out more about quotients, including the quotient map, and prove the Isomorphism Theorem.

# Groups Lecture 11

in which we define normal subgroups, explore groups of order 6 and make a start on quotients.