Alternating Group on 4 Letters/Subgroups/Examples
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Examples of Subgroups of the Alternating Group on $4$ Letters
Order $3$
Let $P$ denote the subset of $A_4$:
- $P := \set {e, a, p}$
Then $P$ is a subgroup of $A_4$.
Its left cosets are:
| \(\ds P\) | \(=\) | \(\ds \set {e, a, p}\) | ||||||||||||
| \(\ds t P\) | \(=\) | \(\ds \set {t, b, q}\) | ||||||||||||
| \(\ds u P\) | \(=\) | \(\ds \set {u, c, r}\) | ||||||||||||
| \(\ds v P\) | \(=\) | \(\ds \set {v, d, s}\) |
Its right cosets are:
| \(\ds P\) | \(=\) | \(\ds \set {e, a, p}\) | ||||||||||||
| \(\ds P t\) | \(=\) | \(\ds \set {t, c, s}\) | ||||||||||||
| \(\ds P u\) | \(=\) | \(\ds \set {u, d, q}\) | ||||||||||||
| \(\ds P v\) | \(=\) | \(\ds \set {v, b, r}\) |