P.A. Gillet: Abstract Algebra (summary)
These are the lecture notes to the (graduate) course Abstract Algebra. If you have downloaded and/or printed an earlier version of these notes, have a look here what was changed since then:
- 3.12: section completed.
- 3.9–10: sections completed.
- 3.8: more typos removed in the lecture notes.
- 3.6: slides of extensions to the talk online. Corrected typos (and the Proposition about Gal(p) for deg p = 4).
- 3.5–3.8: draft of sections 5–8 of chapter 3 online.
- Homepage down, due to server problems
- 3.1-3.2: added slides for my talks,
HW7: Solutions mostly online.
- HW6: Completed solutions,
2.8: polished ending of Chapter 2,
3.1–3.4: put beginning of Chapter 3 online.
- 2.3-2.4: added exercise questions,
HW5: added solutions.
- server down time; I don't know why (I don't run the hardware). I hope it does not happen too often. If you need things urgently, please write me an e-mail (hoping that I still have internet access).
- 2.1: removed typos,
2.2: added Chinese translations of the main notions.
- 2: put lecture notes for the beginning of chapter 2 online. This should be useful for preparing your talks, but please check for apparant errors.
1.16: marked gap in the proof of left-splitting, i.e.\ note that a left-splitting (in a semi-direct product) is not a group homomorphism. It is a group homomorphism iff the product is a direct product.
- 1.16: Added explicit formula for structure of semi-direct products
- finished chapter 1: groups, polishing the sections 1.13 (normal series), 1.14 (solvability and group extensions), 1.15 (semi-direct products and nilpotent groups). Slides also online.
- added appendix A: summary of linear algebra, including formula for the adjunct elements and geometry of the definition(s) of the orthogonal, unitary, and symplectic groups.
- 1.10&12: added slides.
- 1.9: completed the proof of the Sylow theorem(s). Also changed the definition of p-Sylow subgroups, such that the theorem reads smoothly. But the notions effectively stayed the same.
- 1.7: corrected the class equation of D4.
- 2.5: corrected proof of the Structure Theorem for (finitely generated) Abelian groups (case A∞).
1,2,3: killed the chapter number of the Introduction, thus Groups are now Chapter 1, Rings Chapter 2, and Fields Chapter 3. The topics of your talks remain the same (only the numbers change slightly).
- 2.3: Added pictures of the subgroup structure and mapping pattern for the proofs of the second and third isomorphism theorem.
2.2: removed typos noticed during the lecture.
2.1&2.2.: changed notation of Dn such that τ behaves like a translation (τn = id) and σ is a reflection (σ2 = id, (Ger.) Spiegelung).
lecture slides: the section headers in the outline are links to the slides of the corresponding lecture.
- 2.1: added picture of associativity test,
2.1-2.4: added Chinese translations of the most important notions.
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