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:

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Nov. 21:

Nov. 23: Thanksgiving: no class today.

Nov. 28:

Dec. 1:

Dec. 5:

Dec. 8: