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

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Examples of Cosets

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


Let $H \subseteq D_3$ be defined as:

$H = \set {e, r}$


$e$ 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.