#
Spring Quarter 2017, Math 220A: Course Log.

**Sept. 28:** Course administration. Review of basic notions from 111A.
Group actions.

**Oct. 3.:** Group actions cont. Coset decompositions. Isomorphism theorems.

**
Oct. 5:** Cayley's theorem. G-sets; classification of transitive
G-sets as coset spaces; the orbit-stabiliser theorem.

**Oct. 10:** 2-transitive G-sets and maximal
subgroups. Centralisers, comjugates, normalisers; the class
equation. The number of orbits in a G-set.

**Oct. 12:** Sylow's theorems. The Correspondence Theorem.

**Oct. 17:** Finite p-groups and their basic properties.

**
Oct. 19:** Finite p-groups and their basic properties
cont. Nilpotent groups. The basis theorem for finite abelian groups.

**Oct. 24:** Finite p-gropus have normal subgroups of all possible
orders; partial converse to Lagrange's theorem for prime
powers. Normal chains; the Zassenhaus butterfly lemma.

**
Oct. 26:** The Schreier refinement theorem. Composition
series; the Jordan-Holder theorem. Soluble series and soluble groups.

**Oct. 31:**

**
Nov. 2:**

**Nov. 7:**

**
Nov. 9:**

**Nov. 14:**

**
Nov. 16:**

**Nov. 21:**

**
Nov. 23:** Thanksgiving: no class today.

**Nov. 28:**

**
Dec. 1:**

**Dec. 5:**

**
Dec. 8:**