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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Is $D_{2n}$ isomorphic to $D_n \times \Bbb{Z}_2$ for all $n$? For all odd $n$? [duplicate]

Is $D_{2n}$ isomorphic to $D_n \times \Bbb{Z}_2$ for all $n$? For all odd $n$? I just want to see if my thinking is sound here. My thought process is this. $\mathbb{Z}_2 \cong \{e,j\} \subset D_n$ ...
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Find the centraliser of $D_5$ in $GL_4 (\mathbb{R})$

I want to find the centraliser of $D_5$ in $GL_4 (\mathbb{R})$. I can find the centres of $D_5$, i.e. the subgroups of elements that commute with a particular element just by playing around with its ...
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Understanding the dihedral group

I know that the dihedral group is $$D_{2n} = \{1, r, r^2, \dotsc, r^{n-1}, s, sr, \dotsc, sr^n-1\}$$ where the $r^i$ are rotations and $s$ is a symmetry. Now, what I want to know is what is the ...
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How to show $D_3\oplus D_4$ is not isomorphic to $D_{24}$? [duplicate]

How to show $D_3\oplus D_4$ is not isomorphic to $D_{24}$? Here $D_n$ is the dihedral group of order $2n$. I am not sure how to prove this. I am not very good with the dihedreal groups.
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Automorphism group of disjoint cycle graphs of different lengths

This question is supplementary to another question. From that question, we know that the automorphism group of the $N$ disjoint cycle graphs of same length $n$ is $S_N \wr D_n$. My question: What is ...
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Exponent of the direct sum of finite groups, specifically, $\sum^t_i S_{N_i} \wr D_{m_i}$

I have one general and one specific questions. What is the expression for the exponent of the direct sum of finite groups? What is the exponent of $\sum^t_i S_{N_i} \wr D_{m_i}$? Here, $i, N_i, m_i$ ...
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Terminology for dihedral groups

What notation is most common for the dihedral group of order $2n$? I'm talking about the group of symmetries of a regular $n$-gon. I know that some books call this group $D_n$, and some books call it $...