Question

Is the infinite dihedral group isomorphic to $\mathbb{Z}*\mathbb{Z}$?

score 565 · Answer 1 · 2026-03-26 04:31:07

565

Views

Is the infinite dihedral group isomorphic to $\mathbb{Z}*\mathbb{Z}$?

Published on 26 Mar 2026 - 4:31

score 102 · Answer 2 · 2026-04-08 09:10:26

102

Views

The outcome of part of Exercise 7.1.4 of one of Robinson's books.

Published on 08 Apr 2026 - 9:10

score 39 · Answer 3 · 2026-03-26 07:55:20

39

Views

Matrix and Groups Question Solution Check

Published on 26 Mar 2026 - 7:55

score 122 · Answer 4 · 2026-03-28 18:15:54

122

Views

Does there exist some isomorphism from $Q_8$ to $\Bbb Z_4 \times\Bbb Z_2$?

Published on 28 Mar 2026 - 18:15

score 55 · Answer 5 · 2026-03-28 20:07:13

55

Views

Show subgroup isomorphic to direct product

Published on 28 Mar 2026 - 20:07

score 159 · Answer 6 · 2022-02-26 14:28:05

159

Views

What is the question "If G is group of order 360 what are the possible isomorphism types of the Sylow p-subgroups for p=2,3,5,7?" really asking?

Published on 26 Feb 2022 - 14:28

score 56 · Answer 7 · 2026-04-04 20:05:19

56

Views

Showing Groups of Homomorphisms are Isomorphic

Published on 04 Apr 2026 - 20:05

score 53 · Answer 8 · 2026-03-29 09:11:18

53

Views

I guess $G/N\cong G'/N'$ doesn't hold in this case, but I cannot prove that.

Published on 29 Mar 2026 - 9:11

score 68 · Answer 9 · 2026-03-30 05:13:44

68

Views

For a Lie-group G and embedded Lie-subgroups K < H < G, prove that $\pi:G/K \rightarrow G/H$ is a surjective smooth submersion

Published on 30 Mar 2026 - 5:13

score 46 · Answer 10 · 2026-04-08 06:02:45

46

Views

Is the group quotient well defined?

Published on 08 Apr 2026 - 6:02

score 66 · Answer 11 · 2022-03-07 22:35:10

66

Views

Prove or disprove : i) $(\mathbf{S},+,.)\cong (\mathbf{R},+,.)$ (as rings) ii) $(\mathbf{S},+)\cong (\mathbf{R},+)$ (as groups)

Published on 07 Mar 2022 - 22:35

score 78 · Answer 12 · 2022-03-09 01:59:51

78

Views

Prove that $\hspace{1mm} (\mathbb{R}^{n+1} \setminus\{0\})/{]0, \infty[}\cong\mathbb{S}^n$

Published on 09 Mar 2022 - 1:59

score 76 · Answer 13 · 2022-03-10 17:26:03

76

Views

Isomorphism of $\mathbb{Z}_{30}$ to $ \mathbb{Z}_2\times \mathbb{Z}_3\times \mathbb{Z}_5$

Published on 10 Mar 2022 - 17:26

score 25 · Answer 14 · 2026-04-07 00:22:58

25

Views

If $(\mathbb{Z}, +) \cong (C_\infty, \cdot)$, then $\exists K$ such that $K \trianglelefteq C_\infty$ and $K \cong 2\mathbb{Z}$?

Published on 07 Apr 2026 - 0:22

score 66 · Answer 15 · 2026-03-29 10:49:09

66

Views

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

List Question

Is the infinite dihedral group isomorphic to $\mathbb{Z}*\mathbb{Z}$?

The outcome of part of Exercise 7.1.4 of one of Robinson's books.

Matrix and Groups Question Solution Check

Does there exist some isomorphism from $Q_8$ to $\Bbb Z_4 \times\Bbb Z_2$?

Show subgroup isomorphic to direct product

What is the question "If G is group of order 360 what are the possible isomorphism types of the Sylow p-subgroups for p=2,3,5,7?" really asking?

Showing Groups of Homomorphisms are Isomorphic

I guess $G/N\cong G'/N'$ doesn't hold in this case, but I cannot prove that.

For a Lie-group G and embedded Lie-subgroups K < H < G, prove that $\pi:G/K \rightarrow G/H$ is a surjective smooth submersion

Is the group quotient well defined?

Prove or disprove : i) $(\mathbf{S},+,.)\cong (\mathbf{R},+,.)$ (as rings) ii) $(\mathbf{S},+)\cong (\mathbf{R},+)$ (as groups)

Prove that $\hspace{1mm} (\mathbb{R}^{n+1} \setminus\{0\})/{]0, \infty[}\cong\mathbb{S}^n$

Isomorphism of $\mathbb{Z}_{30}$ to $ \mathbb{Z}_2\times \mathbb{Z}_3\times \mathbb{Z}_5$

If $(\mathbb{Z}, +) \cong (C_\infty, \cdot)$, then $\exists K$ such that $K \trianglelefteq C_\infty$ and $K \cong 2\mathbb{Z}$?

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

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