Coset/Examples/Symmetry Group of Equilateral Triangle/Cosets of Reflection Subgroup/Transversals

Examples of Cosets
Consider the symmetry group of the equilateral triangle $D_3$.


 * SymmetryGroupEqTriangle.png

Let $H \subseteq D_3$ be defined as:
 * $H = \set {e, r}$

where:
 * $e$ denotes the identity mapping
 * $r$ denotes reflection in the line $r$.

Some of the left transversals of $H$ are given by:


 * $\set {e, s, t}$
 * $\set {e, q, p}$
 * $\set {r, s, p}$

and so on.