Spring Quarter 2017, Math 220A: Course Log.
Sept. 28: Course administration. Review of basic notions from 111A.
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.
Nov. 23: Thanksgiving: no class today.