Chapter 5
Permutations




  1. Symmetric groups

  2. Cycles

  3. Alternating groups

  4. Exercises

  5. Summary of Chapter 5


In this chapter we study the bijections of a finite set V into itself. The analysis of these bijections, called permutations, yields a tool to describe symmetry. This includes, for example, the description of the symmetries of a quadrangle as bijections of the 4 vertices. This description will appear in detail in Chapter 8, where we deal with groups of permutations.

Section 5.1
Symmetric groups
  1. Maps
  2. Permutation
  3. Notation for permutations

Section 5.2
Cycles
  1. Fix and support
  2. Cycles
  3. Cycle structure
  4. Conjugation
  5. Transpositions

Section 5.3
Alternating groups
  1. Sign
  2. Sign is multiplicative
  3. Alternating group
  4. 3-cycles