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

Examples of Cosets

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

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.

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 6.3$. Index. Transversals: Example $116$