Determine the group of symmetries of the picture, giving a set of generators.
Can you give me any hint please?
2026-03-24 19:08:55.1774379335
Determine the group of symmetries, giving a set of generators.
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Since the OP has now figured this out, I will post an answer.
Let $D = D_4$ be the group of symmetries of the square.
We are looking for the subgroup $G$ of $D$ that preserve the decorations. By inspection, rotations preserve the decorations, so $G$ contains the rotation subgroup $\mathcal R$. The subgroup $\mathcal R$ has index 2 in $D$, so either $G = \mathcal R$ or $G = D$. Since, again by inspection, there is a reflection that does not preserve the decorations, $G \ne D$. Hence $G = \mathcal R$.