List questions from dihedral-groups

66

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Let $G=D_8\times\mathbb{Z_6}$ and $N=D_8\times\{0\}$. Prove that $G/N$ is isomorphic to $\mathbb{Z}_6$.

Published on 29 Mar 2026 - 10:49

157

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Why must a group with presentation $\langle r,s \mid r^n=s^2=1,rs=sr^{-1}\rangle$ have exactly $2n$ elements?

Published on 23 Mar 2022 - 16:46

136

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Proof verification of Dummit and Foote exercise 1.6.24

Published on 28 Mar 2022 - 16:05

178

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When is $D_n\approx\operatorname{Aut}(D_n)$?

Published on 29 Mar 2022 - 13:06

174

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Question on the decomposition of a representation of $D_n$ into irreducible representations.

Published on 03 Apr 2022 - 21:00

93

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Show the function between the dihedral groups is well defined

Published on 03 Apr 2022 - 22:15

179

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Check if kernel and image for dihedral group defined correctly

Published on 14 Apr 2022 - 22:43

61

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Question about center of dihedral group

Published on 16 Apr 2022 - 20:55

92

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Dummit & Foote Chapter 1.2 Exercise 17 (Group Presentations)

Published on 20 Apr 2022 - 13:29

69

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How would you describe the symmetries/group actions on the $\ell_p$ circle?

Published on 26 Mar 2026 - 14:32

75

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Let $n$ be an even number. Prove that $D_n/Z(D_n)$ is isomorphic to $D_{n/2}$.

Published on 29 Apr 2022 - 5:07

30

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Formula for the number of ways to choose $n$ digits from $k$ possible digits such that the selection contains no repeats under permutation

Published on 02 May 2022 - 1:30

89

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Proof idea: $S_3 \cong D_3$

Published on 12 May 2022 - 3:11

217

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Understanding von Dyck's theorem

Published on 17 May 2022 - 2:37

68

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What is actually the center of semi dihedral group $SD_{24}$?

Published on 20 May 2022 - 10:11

List Question

Let $G=D_8\times\mathbb{Z_6}$ and $N=D_8\times\{0\}$. Prove that $G/N$ is isomorphic to $\mathbb{Z}_6$.

Why must a group with presentation $\langle r,s \mid r^n=s^2=1,rs=sr^{-1}\rangle$ have exactly $2n$ elements?

Proof verification of Dummit and Foote exercise 1.6.24

When is $D_n\approx\operatorname{Aut}(D_n)$?

Question on the decomposition of a representation of $D_n$ into irreducible representations.

Show the function between the dihedral groups is well defined

Check if kernel and image for dihedral group defined correctly

Question about center of dihedral group

Dummit & Foote Chapter 1.2 Exercise 17 (Group Presentations)

How would you describe the symmetries/group actions on the $\ell_p$ circle?

Let $n$ be an even number. Prove that $D_n/Z(D_n)$ is isomorphic to $D_{n/2}$.

Formula for the number of ways to choose $n$ digits from $k$ possible digits such that the selection contains no repeats under permutation

Proof idea: $S_3 \cong D_3$

Understanding von Dyck's theorem

What is actually the center of semi dihedral group $SD_{24}$?

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