Notes - Groups HT23, Equivalence relations
Flashcards
What equivalence relation defines congruency in modular arithmetric?
\[x \equiv y \pmod n \iff n | (x-y)\]
Can you define the equivalence class of $x$ under an equivalence relation “$\sim$” on $S$?
\[\bar x = \\{y \in S : x \sim y\\}\]
Can you define the conjugacy class of $x$ in some group $G$?
\[\bar x = \\{y \in G : \exists p \in G \text{ s.t. } x = p^{-1}yp\\}\]
Proofs
Prove that the equivalence classes on a set $S$ form a partition of that set.
Todo.