# 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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### Find $|{\rm Aut}(D_8\times S_3)|$ using a particular result about Remak decompositions.

This is Exercise 3.3.9 of Robinson's "A Course in the Theory of Groups (Second Edition)". According to Approach0, it is new to MSE. The Details: On page 6, ibid, the dihedral group $D_{2n}$ ...
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### Ascending central series for $D_8$

My Group Theory notes give as definition for an ascending series: $G_0, G_1,...,G_n \unlhd G$ such that $\{1\} = G_0 \unlhd G_1 \unlhd ... \unlhd G_n=G$ and $G_{i+1}/ G_{i} \subset Z(G/G_{i})$. As an ...
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### Importance of studying certain graphs on the dihedral group

I am actually not sure if this is the right platform to ask this, but I hope someone can enlighten me. I am an undergraduate math student, and I recently started reading academic papers on graph ...
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### Do overlapping left and right coset spaces have a name?

I have been studying they symmetries of the square, D₄. I would like to use the subgroups that are not normal to make a coset space, but since they are not normal, the right coset space is different ...
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### Prove that $D'_n=\langle x^2\rangle$

I want to check if my solution to one problem from my group theory course is valid. The problem is: Given $D_n=\{x^iy^j:0\leq i<n,0\leq j<2\}$, prove that $D'_n=\langle x^2\rangle$. My attempt ...
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### Prove three statements about the dihedral group $D_6$

I'm trying to solve this problem from my group theory course: Consider the dihedral group $D_6$ of isometries of the euclidean plane which fix a regular hexagon: (a) Prove that this group is ...
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### Finite group generated by two different order $2$ elements is $\cong$ to $\mathbb{Z}_2^2$ or $D_n$

I'm trying to solve this problem from my group theory course: Given $G$ finite group generated by two different order $2$ elements. Prove that $G\cong \mathbb{Z}_2^2$ or $G\cong D_n$ for some \$n\geq ...