Composition Series/Examples/Symmetric Group S3

Example of Composition Series

There is $1$ composition series of the symmetric group on $3$ letters $S_3$, up to isomorphism:

$\set e \lhd A_3 \lhd S_3$

where $A_3$ is the alternating group on $3$ letters.

Hence $S_3$ is (trivially) solvable.

Sources

• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Symmetric Groups: $\S 84 \alpha$