Size of coset equals size of subset

Dependencies:

1. Coset

Let $H$ be a subset of a group $G$. Let $g \in G$. Then $|gH| = |H|$.

Proof

Each element $h \in H$ has a corresponding value $gh \in gH$. There cannot be two $h$ which map to the same $gh$, because $gh_1 = gh_2 \Rightarrow h_1 = h_2$. Therefore, $|gH| = |H|$.

Dependency for:

1. Lagrange's Theorem

Info:

• Depth: 2
• Number of transitive dependencies: 2

Transitive dependencies:

1. Group
2. Coset