Question

How to find the order of a dihedral group made up of two elements of order $2$?

score 55 · Answer 1 · 2020-09-09 22:54:19

55

Views

How to find the order of a dihedral group made up of two elements of order $2$?

Published on 09 Sep 2020 - 22:54

score 52 · Answer 2 · 2020-09-17 14:40:17

52

Views

Equivalent definitions to $D_{n}$

Published on 17 Sep 2020 - 14:40

score 368 · Answer 3 · 2020-09-21 22:30:20

368

Views

Can you show why is a dihedral group homomorphic to a symmetric group?

Published on 21 Sep 2020 - 22:30

score 113 · Answer 4 · 2020-09-23 16:24:29

113

Views

Deriving the group cohomology of $D_{2n}$ from that of $D_2$

Published on 23 Sep 2020 - 16:24

score 59 · Answer 5 · 2020-09-24 22:12:08

59

Views

Showing that for $n \geq 3$, $Z(D_{2n}) = 1$ for odd $n$ and $Z(D_{2n}) = \{1, r^{\frac{n}{2}}\}$ for even $n$.

Published on 24 Sep 2020 - 22:12

score 263 · Answer 6 · 2020-09-26 00:43:01

263

Views

Understanding how reflection acts on rotation in $D_{6}.$

Published on 26 Sep 2020 - 0:43

score 123 · Answer 7 · 2020-09-26 03:29:46

123

Views

Understanding why proving a hint will prove that $D_{6} \cong S_{3} \times \mathbb{Z}_{2}.$

Published on 26 Sep 2020 - 3:29

score 62 · Answer 8 · 2020-09-26 14:30:07

62

Views

Identify the isomorphism of the group $D_6 / \langle\rho ^3\rangle$.

Published on 26 Sep 2020 - 14:30

score 63 · Answer 9 · 2020-10-06 02:45:11

63

Views

Proving that the stabilizer of $\{2,4,6\}$ in $D_{6}$ is isomorphic to $S_{3}.$

Published on 06 Oct 2020 - 2:45

score 42 · Answer 10 · 2020-10-06 17:06:23

42

Views

What are the fixed points of $S = \{A, B,C,D,E \}$ under the action of $D_4\ ?$

Published on 06 Oct 2020 - 17:06

score 40 · Answer 11 · 2026-03-28 04:34:26

40

Views

Showing that $D_{6}$ has a two element subgroup, isomorphic to $\Bbb Z_2$, whose intersection with $S_3$ is trivial.

Published on 28 Mar 2026 - 4:34

score 1.9k · Answer 12 · 2020-10-14 13:22:33

1.9k

Views

how to list elements of a dihedral group $D_n$

Published on 14 Oct 2020 - 13:22

score 311 · Answer 13 · 2026-03-25 16:02:24

311

Views

Is the dihedral group $D_{2n}$ a subgroup of $GL_2(\mathbb{C})$?

Published on 25 Mar 2026 - 16:02

score 2.5k · Answer 14 · 2020-10-17 19:06:17

2.5k

Views

Find all the normal subgroups of the dihedral group $D_4$ (of order $8$) and find all the factor groups up to isomorphism.

Published on 17 Oct 2020 - 19:06

score 126 · Answer 15 · 2020-10-20 02:56:08

126

Views

Let $G = D_4 \times \mathbb{Z}_3$. Prove that $G \space / \space Z(G)$ is isomorphic to $\mathbb{Z}_2 \times \mathbb{Z}_2$.

Published on 20 Oct 2020 - 2:56

List Question

How to find the order of a dihedral group made up of two elements of order $2$?

Equivalent definitions to $D_{n}$

Can you show why is a dihedral group homomorphic to a symmetric group?

Deriving the group cohomology of $D_{2n}$ from that of $D_2$

Showing that for $n \geq 3$, $Z(D_{2n}) = 1$ for odd $n$ and $Z(D_{2n}) = \{1, r^{\frac{n}{2}}\}$ for even $n$.

Understanding how reflection acts on rotation in $D_{6}.$

Understanding why proving a hint will prove that $D_{6} \cong S_{3} \times \mathbb{Z}_{2}.$

Identify the isomorphism of the group $D_6 / \langle\rho ^3\rangle$.

Proving that the stabilizer of $\{2,4,6\}$ in $D_{6}$ is isomorphic to $S_{3}.$

What are the fixed points of $S = \{A, B,C,D,E \}$ under the action of $D_4\ ?$

Showing that $D_{6}$ has a two element subgroup, isomorphic to $\Bbb Z_2$, whose intersection with $S_3$ is trivial.

how to list elements of a dihedral group $D_n$

Is the dihedral group $D_{2n}$ a subgroup of $GL_2(\mathbb{C})$?

Find all the normal subgroups of the dihedral group $D_4$ (of order $8$) and find all the factor groups up to isomorphism.

Let $G = D_4 \times \mathbb{Z}_3$. Prove that $G \space / \space Z(G)$ is isomorphic to $\mathbb{Z}_2 \times \mathbb{Z}_2$.

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