Question

Prove that $\mathbb{Z}[\sqrt 2]/(3+\sqrt 2)$ isomorphic to $\mathbb{Z}_7$

score 1.4k · Answer 1 · 2017-04-03 18:32:19

1.4k

Views

Prove that $\mathbb{Z}[\sqrt 2]/(3+\sqrt 2)$ isomorphic to $\mathbb{Z}_7$

Published on 03 Apr 2017 - 18:32

score 60 · Answer 2 · 2017-04-04 03:43:07

60

Views

How would I show that $SO^{+}(n,1) / SO(n) \approx \mathbb{H}$?

Published on 04 Apr 2017 - 3:43

score 178 · Answer 3 · 2023-01-31 15:42:35

178

Views

Does $G/K \cong H$ imply that $G \cong H\times K$ for normal $H,K$?

Published on 31 Jan 2023 - 15:42

score 93 · Answer 4 · 2026-02-23 10:06:16

93

Views

Let $G$ be a subgroup of $E(2)$ and suppose that $T$ is the translation subgroup of $G$. Prove that the point group of $G$ is isomorphic to $G/T$.

Published on 23 Feb 2026 - 10:06

score 47 · Answer 5 · 2023-02-02 16:32:17

47

Views

inverse elements in quotient ring $\mathbb{Z}/_{\langle 560 \rangle}$

Published on 02 Feb 2023 - 16:32

score 75 · Answer 6 · 2026-03-25 14:22:37

75

Views

For groups, rings, or $R$-modules $A, B, C$ with $C\subseteq B$, does $A/B \cong A/C$ imply that $B=C$?

Published on 25 Mar 2026 - 14:22

score 62 · Answer 7 · 2023-02-06 17:47:09

62

Views

Finitely generated abelian groups $G,H$ with the same finite quotients (up to isomorphism) are isomorphic

Published on 06 Feb 2023 - 17:47

score 99 · Answer 8 · 2026-03-25 17:44:35

99

Views

Order of $xy$ in various quotients of the free product $G_1 * G_2$, where $x \in G_1, y \in G_2$ are nontrivial

Published on 25 Mar 2026 - 17:44

score 78 · Answer 9 · 2023-02-08 21:13:21

78

Views

Identify the group $(28\mathbb Z + 20\mathbb Z)/20 \mathbb Z$

Published on 08 Feb 2023 - 21:13

score 79 · Answer 10 · 2023-02-15 13:14:50

79

Views

How to I take the quotient $GL^+(2,\mathbb{R})/SO(2,\mathbb{R})$

Published on 15 Feb 2023 - 13:14

score 53 · Answer 11 · 2023-02-18 03:17:18

53

Views

When do $H_1 \cong H_2$ and $K_1 \cong K_2$ imply $F(H_1,K_1) \cong F(H_2,K_2)$?

Published on 18 Feb 2023 - 3:17

score 78 · Answer 12 · 2023-03-08 13:19:05

78

Views

Coset of $[18]$ in $\Bbb Z_{55}/11\Bbb Z_{55}?$

Published on 08 Mar 2023 - 13:19

score 59 · Answer 13 · 2023-03-21 19:58:20

59

Views

Proof that all Quotient Groups are Abelian- where is my error?

Published on 21 Mar 2023 - 19:58

score 125 · Answer 14 · 2023-03-22 18:22:21

125

Views

If the cardinality of the quotient set of a subgroup is $1$ does that mean that the subgroup is equal to the whole group?

Published on 22 Mar 2023 - 18:22

score 96 · Answer 15 · 2023-03-24 11:38:41

96

Views

Does it make sense to talk about a factor group by a non-subgroup?

Published on 24 Mar 2023 - 11:38

List Question

Prove that $\mathbb{Z}[\sqrt 2]/(3+\sqrt 2)$ isomorphic to $\mathbb{Z}_7$

How would I show that $SO^{+}(n,1) / SO(n) \approx \mathbb{H}$?

Does $G/K \cong H$ imply that $G \cong H\times K$ for normal $H,K$?

Let $G$ be a subgroup of $E(2)$ and suppose that $T$ is the translation subgroup of $G$. Prove that the point group of $G$ is isomorphic to $G/T$.

inverse elements in quotient ring $\mathbb{Z}/_{\langle 560 \rangle}$

For groups, rings, or $R$-modules $A, B, C$ with $C\subseteq B$, does $A/B \cong A/C$ imply that $B=C$?

Finitely generated abelian groups $G,H$ with the same finite quotients (up to isomorphism) are isomorphic

Order of $xy$ in various quotients of the free product $G_1 * G_2$, where $x \in G_1, y \in G_2$ are nontrivial

Identify the group $(28\mathbb Z + 20\mathbb Z)/20 \mathbb Z$

How to I take the quotient $GL^+(2,\mathbb{R})/SO(2,\mathbb{R})$

When do $H_1 \cong H_2$ and $K_1 \cong K_2$ imply $F(H_1,K_1) \cong F(H_2,K_2)$?

Coset of $[18]$ in $\Bbb Z_{55}/11\Bbb Z_{55}?$

Proof that all Quotient Groups are Abelian- where is my error?

If the cardinality of the quotient set of a subgroup is $1$ does that mean that the subgroup is equal to the whole group?

Does it make sense to talk about a factor group by a non-subgroup?

Trending Questions

Popular # Hahtags

Popular Questions