Coset

Dependencies:

1. Group

Let $H$ be a subset of a group $G$ and $g \in G$. Then the left coset of $H$ with representative $G$ is the set $gH = \{gh: h \in H\}$. Similarly, the right coset of $H$ with representative $G$ is the set $Hg = \{hg: h \in H\}$.

Usually (unless stated otherwise), $H$ is a subgroup of $G$.

Dependency for:

1. Normal Subgroup
2. For subset H of a group, a(bH) = (ab)H and (aH)b = a(Hb)
3. Two cosets are either identical or disjoint
4. gH = H iff g in H
5. Lagrange's Theorem
6. Inverse of a coset
7. Size of coset equals size of subset

Info:

• Depth: 1
• Number of transitive dependencies: 1

Transitive dependencies:

1. Group