Question

Consider a reflection as an element of the permutation group of the vertices of a regular (2n + 1)-gon. Is the permutation even or odd?

score 379 · Answer 1 · 2026-03-28 12:33:28

379

Views

Consider a reflection as an element of the permutation group of the vertices of a regular (2n + 1)-gon. Is the permutation even or odd?

Published on 28 Mar 2026 - 12:33

score 235 · Answer 2 · 2026-03-29 04:41:26

235

Views

Sylow-$2$ Subgroups of a simple group of order 168

Published on 29 Mar 2026 - 4:41

score 29 · Answer 3 · 2022-11-14 16:31:49

29

Views

Show that for even integers $ n $ there exists an element $ g \in D_{n} $ : $ \operatorname{ord}(g)=2 $ and $ \operatorname{sgn}(\varphi(g))=1 $

Published on 14 Nov 2022 - 16:31

score 50 · Answer 4 · 2022-11-15 14:53:35

50

Views

Find different symmetries of $D_4$ by composition of component symmetries.

Published on 15 Nov 2022 - 14:53

score 50 · Answer 5 · 2022-11-16 06:10:52

50

Views

Doubts in the action of $D_4$ on the set of $2$-colorings of a square.

Published on 16 Nov 2022 - 6:10

score 133 · Answer 6 · 2022-11-19 18:27:53

133

Views

Question on the definition of the Dihedral groups

Published on 19 Nov 2022 - 18:27

score 106 · Answer 7 · 2022-11-20 22:06:39

106

Views

Embedding of dihedral group in $\mathbb{Z}_{2^n}$

Published on 20 Nov 2022 - 22:06

score 42 · Answer 8 · 2022-12-13 23:40:07

42

Views

Show that $D_{2^n}/Z(D_{2^n})\cong D_{2^{n-1}}$.

Published on 13 Dec 2022 - 23:40

score 58 · Answer 9 · 2026-03-26 12:34:02

58

Views

Fitting length of Dihedral groups

Published on 26 Mar 2026 - 12:34

score 191 · Answer 10 · 2026-03-29 05:43:36

191

Views

Show that the $D_{3h}$ prism is given by the direct product $D_{3h}=D_3 \otimes C_s$

Published on 29 Mar 2026 - 5:43

score 174 · Answer 11 · 2022-12-26 08:23:50

174

Views

Prove that all dihedral groups of degree $4$ are isomorphic

Published on 26 Dec 2022 - 8:23

score 130 · Answer 12 · 2022-12-30 12:58:52

130

Views

Step in a proof that $G:=\langle x,y \mid x^n,y^2, (xy)^2\rangle$ is isomorphic to the dihedral group $D_n$

Published on 30 Dec 2022 - 12:58

score 61 · Answer 13 · 2023-01-01 14:23:21

Let $a,b\in D_4$ and such that $ba=a^{3}b$. Prove that if $0\leq i<4$ and $0\leq j<2$, then $a^ib^ja^{i_1}b^{j_1}=a^{i+3i_1}b^{j+j_1}$

score 78 · Answer 14 · 2023-01-05 21:31:09

78

Views

Looking for a subgroup $H$ of $D_{2019}$ with the following properties:

Published on 05 Jan 2023 - 21:31

score 79 · Answer 15 · 2023-01-27 06:47:26

79

Views

Are the mean and variance of a dihedral angle periodic?

Published on 27 Jan 2023 - 6:47

List Question

Consider a reflection as an element of the permutation group of the vertices of a regular (2n + 1)-gon. Is the permutation even or odd?

Sylow-$2$ Subgroups of a simple group of order 168

Show that for even integers $ n $ there exists an element $ g \in D_{n} $ : $ \operatorname{ord}(g)=2 $ and $ \operatorname{sgn}(\varphi(g))=1 $

Find different symmetries of $D_4$ by composition of component symmetries.

Doubts in the action of $D_4$ on the set of $2$-colorings of a square.

Question on the definition of the Dihedral groups

Embedding of dihedral group in $\mathbb{Z}_{2^n}$

Show that $D_{2^n}/Z(D_{2^n})\cong D_{2^{n-1}}$.

Fitting length of Dihedral groups

Show that the $D_{3h}$ prism is given by the direct product $D_{3h}=D_3 \otimes C_s$

Prove that all dihedral groups of degree $4$ are isomorphic

Step in a proof that $G:=\langle x,y \mid x^n,y^2, (xy)^2\rangle$ is isomorphic to the dihedral group $D_n$

Let $a,b\in D_4$ and such that $ba=a^{3}b$. Prove that if $0\leq i<4$ and $0\leq j<2$, then $a^ib^ja^{i_1}b^{j_1}=a^{i+3i_1}b^{j+j_1}$

Looking for a subgroup $H$ of $D_{2019}$ with the following properties:

Are the mean and variance of a dihedral angle periodic?

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