Groups HT23, Equivalence relations
Flashcards
What equivalence relation defines congruency in modular arithmetic?
\[x \equiv y \pmod n \iff n \vert (x-y)\]
@Define the equivalence class of $x$ under an equivalence relation “$\sim$” on $S$.
\[\bar x = \{y \in S : x \sim y\}\]
@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.