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

# normal subgroup

# Groups Lecture 17

*in which we explore conjugacy classes in and , and prove that 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 and , and prove that 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.
*