Lectures 20
Permutation matrix: definition and examples. More on cosets (left and right).
Lectures 21
Properties of cosets. Lagrange's theorem (again) and corollaries: including the result that groups of prime order are cyclic.
Lectures 22 & 23
Normal subgroups. Definition in terms of cosets and as gNg^{-1} and examples. The product of cosets and the quotient group defined from the set of cosets. The group axioms for the quotient group and an example based on the group D_8 of symmetries of the square. Beginning discussion of isomorphisms.