6) Conjugacy Flashcards
What is the Conjugacy action of a group
What are conjugacy classes and conjugate elements
Conjugacy classes - the orbits of the conjugacy
action (denoted g^G)
Conjugate elements - two elements g, h ∈ G are called
conjugate if they lie in the same conjugacy class, in other words, if there exists an element k ∈ G with kgk−1 = h
How do general properties of group actions apply specifically to conjugacy in groups
What property do conjugate elements share
If two group elements are conjugate then they have the same order
What are Centralisers
Describe the proof that conjugate elements have the same order
Why is the centraliser of an element considered a subgroup of a group
Because the centraliser is a stabiliser it is a subgroup
What is the centre of a group
How is the size of a conjugacy class related to the centraliser of an element in a group
What is the Class Equation
Describe the proof of the class equation
What determines if two permutations are conjugate in the symmetric group
