Symmetry Group of Equilateral Triangle is Solvable

Theorem

The symmetry group $D_3$ of the equilateral triangle is a solvable group.

Proof

From Symmetry Group of Equilateral Triangle is Symmetric Group, $D_3$ is the symmetric group on $3$ letters $S_3$.

The result follows from Examples of Composition Series: Symmetric Group $S_3$.

$\blacksquare$

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): soluble group (US: solvable group)