Wednesday Oct 25 - Wednesday Nov 1

I had some delay creating this blog (Blogger kept being down or slow). In general I will try to keep these reasonably up-to-date.

Wed Oct 25

Definitions of group, homomorphism, kernel, subgroup, normal subgroup, product group, coset space, automorphism.
Definitions of Aut(G) for G a group, and semidirect product.

Mon Oct 30

Definition of group isomorphism. Recognition theorem for semidirect producst. Many examples thereof, including dihedral groups and the Euclidean group of motions. Short exact sequences of groups. Groups of order up to 10 (no proofs).

Wed Nov 1

Sym(X) = permutations of X. Two equivalent definitions of left G-set.
Right G-sets. Which, theorem, are equivalent to left G-sets (using group inverse).
G-orbits, X/G.
G acts on X, H acts on Y -> GxH acts on XxY. Diagonal action.