Abstract Algebra

Notes about Abstract Algebra from Artin and Dummit-Foote.

• Symmetric Group $S_n$: Permutation of set of indices $\{1,2,\dots ,n\}$.
  • Finite group of order $n!$
• Symmetric group of a set $T$, defined as $\text{Sym}(T)=\{\text{all bijections }a:T\to T\}$ under composition $a\circ b(t)=a(b(t))$, where $a,b$ are bijections of the set.
  • This can be referred to as automorphism group of T, written as $\text{Aut}(T)$
• Subgroup

References

• Honors Abstract Algebra I - Math 5590H - 5111 - Autumn 2024
• Math 331-1: Abstract Algebra Lecture Notes
• Abstract Algebra - Free Harvard Courses
• Readings | Algebra I | Mathematics | MIT OpenCourseWare