# Questions tagged [dihedral-groups]

For questions on dihedral groups, the group of symmetries of a regular polygon, including both rotations and reflections

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### Why a dihedral group isn't a normal subgroup of a permutation group?

A claim says that two permutations are conjugate when they have the same type. I don't know how to show (using this claim) that a dihedral group $D_{2n}$ isn't a normal subgroup of a permutation group ...
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### Dihedral group $D_2$

Can a dihedral group $D_2$ be a set of transformations of a line segment? If it can then what are the reflections? No matter how I think about reflecting it I always get either the identity or the ...
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### A question about dihedral group

The presentation of the dihedral group is $$D_{2n}= \langle r,s \mid r^{n}=s^{2}=1, (sr)^2=1 \rangle.$$ Now, let $G$ be a group of order $2n$. Is it true that if $G$ contains two elements $a,b$ such ...
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### Dihedral group for arbitrary polygon

Is a dihedral group only considered for shapes that when reflected or rotated fit exactly back into place of the original image? My confusion arises from this wikipedia article and specifically from ...
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### Inverse element of dihedral group… [closed]

I am having a hard time conceptualizing what is the inverse element of, for example, a dihedral group on the equilateral triangle. Can anyone explain this to me?
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### Dihedral group understanding

I have just started reading Abstract Algebra by Dummit and Foote and I have been stuck on their explanation of dihedral groups. On page 23 Dihedral Groups there are 3 paragraphs(one paragraph is at ...
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### Can we build a D4 matrix representation with ${\mathbb Z_2}^{4\times 4}$ matrices?

If we look at the Dihedral 4 group. There exists a trivial matrix representation that also makes it very easy to define group action on vectors: simply use 2x2 rotation matrices for the cyclic part ...
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