Question

Let $R_2 = \{1, \rho_2 \} \subset D_4$. Show that $R_2$ is a normal subgroup of $D_4$.

score 124 · Answer 1 · 2021-09-05 17:38:57

124

Views

Let $R_2 = \{1, \rho_2 \} \subset D_4$. Show that $R_2$ is a normal subgroup of $D_4$.

Published on 05 Sep 2021 - 17:38

score 1.1k · Answer 2 · 2021-09-13 19:09:43

1.1k

Views

Proving $r^i s = sr^{-i}$ in $D_{2n}$

Published on 13 Sep 2021 - 19:09

score 778 · Answer 3 · 2021-09-15 22:12:59

778

Views

The elements of the dihedral group $D_{24}$ and their orders.

Published on 15 Sep 2021 - 22:12

score 57 · Answer 4 · 2026-03-29 02:34:51

57

Views

How do I identify the quotient groups in $D_{12}?$

Published on 29 Mar 2026 - 2:34

score 147 · Answer 5 · 2026-02-23 10:47:22

147

Views

Polya Enumeration: Generate Configurations off of Cycle Index

Published on 23 Feb 2026 - 10:47

score 323 · Answer 6 · 2021-09-17 10:03:18

323

Views

Commutators in the infinite dihedral group

Published on 17 Sep 2021 - 10:03

score 37 · Answer 7 · 2021-09-19 12:53:29

37

Views

Understanding why we need "mod n" in the definition of $r(j)$?

Published on 19 Sep 2021 - 12:53

score 72 · Answer 8 · 2021-09-19 15:28:29

72

Views

Why the action of $D_{2n}$ on $\{a_i\}$ should look like this?

Published on 19 Sep 2021 - 15:28

score 222 · Answer 9 · 2021-09-22 18:03:54

222

Views

Checking that $\cdot: D_{2n}\times \{1,2,\ldots,n\} \rightarrow\{1,2,\ldots,n\}$ given by $(\alpha , i) \mapsto\sigma_{\alpha}(i)$ is a group action

Published on 22 Sep 2021 - 18:03

score 56 · Answer 10 · 2026-03-28 16:26:34

56

Views

If $n$ is odd prove that $D_{2n} \cong \langle a^n \rangle \times \langle a^2,b\rangle.$

Published on 28 Mar 2026 - 16:26

score 65 · Answer 11 · 2021-10-06 13:59:58

65

Views

How do we prove that $\tau \rho = \rho^{-1} \tau$ in general for $D_{2n}$

Published on 06 Oct 2021 - 13:59

score 1k · Answer 12 · 2021-10-07 17:59:00

1k

Views

Prove that order of $D_{2n}$ is exactly $2n$

Published on 07 Oct 2021 - 17:59

score 230 · Answer 13 · 2021-10-09 02:34:06

230

Views

Dihedral group as a subgroup of the symmetric group.

Published on 09 Oct 2021 - 2:34

score 82 · Answer 14 · 2021-10-14 05:15:56

82

Views

Show $\Bbb{Z}_{30},\ \Bbb{Z}_5 \times D_3,\ \Bbb{Z}_3 \times D_5$ and $D_{15}$ are not isomorphic where $D_n$ is the dihedral group.

Published on 14 Oct 2021 - 5:15

score 85 · Answer 15 · 2021-10-19 10:22:36

85

Views

Determine whether $D_4/Z(D_4)\otimes Z(D_4)$ is isomorphic to $D_4$

Published on 19 Oct 2021 - 10:22

List Question

Let $R_2 = \{1, \rho_2 \} \subset D_4$. Show that $R_2$ is a normal subgroup of $D_4$.

Proving $r^i s = sr^{-i}$ in $D_{2n}$

The elements of the dihedral group $D_{24}$ and their orders.

How do I identify the quotient groups in $D_{12}?$

Polya Enumeration: Generate Configurations off of Cycle Index

Commutators in the infinite dihedral group

Understanding why we need "mod n" in the definition of $r(j)$?

Why the action of $D_{2n}$ on $\{a_i\}$ should look like this?

Checking that $\cdot: D_{2n}\times \{1,2,\ldots,n\} \rightarrow\{1,2,\ldots,n\}$ given by $(\alpha , i) \mapsto\sigma_{\alpha}(i)$ is a group action

If $n$ is odd prove that $D_{2n} \cong \langle a^n \rangle \times \langle a^2,b\rangle.$

How do we prove that $\tau \rho = \rho^{-1} \tau$ in general for $D_{2n}$

Prove that order of $D_{2n}$ is exactly $2n$

Dihedral group as a subgroup of the symmetric group.

Show $\Bbb{Z}_{30},\ \Bbb{Z}_5 \times D_3,\ \Bbb{Z}_3 \times D_5$ and $D_{15}$ are not isomorphic where $D_n$ is the dihedral group.

Determine whether $D_4/Z(D_4)\otimes Z(D_4)$ is isomorphic to $D_4$

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