# Math 310 — Group Theory About Lectures OnQ About Lectures OnQ

Date Topic Book HomeworkHmwk Practice ProblemsProbs
Sept. 12 Introduction to the course §1   1— 10
14 Counting symmetries of polyhedra §1
15 Axioms §2—3 §2: 3—7; §4: 2— 4
19 Examples of groups §3 1—10
21 More symmetries of algebraic structures §9 1—6
22 Subgroups and generators §5 H1 1—5, 7, 8
26 Order of an element, Cyclic groups §5 A1 10—12
28 Dihedral groups §4 5—9
29 The symmetric group §6 H2 1—5
Oct. 3 More Symmetric Group §6 A2
5 Homomorphisms §16 1—7
6 Isomorphisms §7 H3 1—12
10 The alternating group §6 A3 8—12
12 Cosets §11—12 §11: 1, 2; §12: 3, 8
13 Lagrange's theorem §11 H4 1—5
17 Normal subgroups §15 A4 1, 2, 4 6
19 Quotient groups §15 13
20 The first isomorphism theorem §16 H5
24 The correspondence theorem §16 A5
26 Proof of the correspondence theorem §16
27 Conjugation and conjugacy classes §14 H6 1—5
31 More conjugation §14 A6 6, 9, 12
Nov. 2 Products §10 1—13
3 Semi-direct products §23 H7 8—12
7 Group actions on sets §17 A7 1, 2, 5, 6, 7
9 The orbit-stablizer theorem §17 3, 4,
10 Remembrance Day H8
14 More orbit-stabilizer §17 A8 6, 7, 8
16 Automorphisms of the platonic solids §8 4, 11
17 Symmetries of the icosahedron §8 H9 5, 12
21 p-groups and the Sylow theorems §20 A9 1, 2
23 Proofs of the Sylow theorems §20 3, 9, 10
24 More Sylow theorems §20 H10
28 Groups of elementary order A10
30 Finitely generated abelian groups §21 1—5
Dec. 1 Finite subgroups of SO3 §19 H11 4, 5
5   A11
7
8   H12
13   A12