Abstract Algebra I — Fall 2026

MATH 3551, Section A · MWF 12:00–12:50, Lafayette L107 · first class Wednesday, September 9
Taylor Dupuy · Innovation E439 · office hours TBA

Lectures

Suggested problems, with commentary (PDF)

Text

Dummit and Foote — Abstract Algebra, 3rd edition (Wiley), ISBN 0-471-43334-9. Errata.

Exam Schedule

Midterm 1 (Monday, October 12, in class — §1.1–§3.2)
Midterm 2 (Friday, November 6, in class — §3.3–§4.4)
Midterm 3 (Monday, November 30, in class — §4.5–§5.2)
Final (Thursday, December 17, 10:30 AM–1:15 PM, Lafayette L107 — cumulative)

Practice Exams

Practice Midterm 1 — exam, solutions
Practice Midterm 2 — exam, solutions
Practice Midterm 3 — exam, solutions
Practice Final — exam, solutions

Suggested Problems

Dummit and Foote, 3rd edition, by section. Not collected, not graded. The PDF has the same list with commentary on each problem.

Part I — through Midterm 1 (§1.1–§3.2)

§1.1 Basic Axioms and Examples — 1, 6, 9, 10, 13, 14, 16, 19, 20, 21, 22, 23, 24, 26, 31, 32, 33, 36
§1.2 Dihedral Groups — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17
§1.3 Symmetric Groups — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20
§1.4 Matrix Groups — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
§1.5 The Quaternion Group — 1, 2, 3
§1.6 Homomorphisms and Isomorphisms — 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15, 17, 18, 20, 21, 22, 24, 26
§1.7 Group Actions — 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21
§2.1 Subgroups: Definition and Examples — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
§2.2 Centralizers and Normalizers, Stabilizers and Kernels — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
§2.3 Cyclic Groups and Cyclic Subgroups — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 23, 24, 25, 26
§2.4 Subgroups Generated by Subsets of a Group — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20
§2.5 The Lattice of Subgroups of a Group — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
§3.1 Quotient Groups and Homomorphisms: Definitions and Examples — 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 15, 17, 22, 24, 25, 26, 32, 33, 35, 36, 40, 41, 42
§3.2 More on Cosets and Lagrange's Theorem — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23

Part II — through Midterm 2 (§3.3–§4.4)

§3.3 The Isomorphism Theorems — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
§3.4 Composition Series and the Hölder Program — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
§3.5 Transpositions and the Alternating Group — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
§4.1 Group Actions and Permutation Representations — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
§4.2 Cayley's Theorem — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
§4.3 The Class Equation — 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 22, 23, 24, 25, 28, 29, 30, 33
§4.4 Automorphisms — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20

Part III — through Midterm 3 (§4.5–§5.2)

§4.5 The Sylow Theorems — 1, 2, 3, 4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 29, 33, 34, 36
§4.6 The Simplicity of A_n — 1, 2, 3, 4, 5, 6, 7, 8
§5.1 Direct Products — 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 18
§5.2 The Fundamental Theorem of Finitely Generated Abelian Groups — 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16

Part IV — final only (§5.4, §5.5, §6.1)

§5.4 Recognizing Direct Products — 1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20
§5.5 Semidirect Products — 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 16, 17, 20, 21, 24
§6.1 p-groups, Nilpotent Groups, and Solvable Groups — 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 14, 15, 17, 19, 23, 26

Previous versions of this course

Notes

Nothing yet.