Question

Computation of Amalgamated Product $\mathbb{Z}_4 \ast_{\mathbb{Z}_2} \mathbb{Z}_6.$

score 191 · Answer 1 · 2026-03-25 17:39:41

191

Views

Computation of Amalgamated Product $\mathbb{Z}_4 \ast_{\mathbb{Z}_2} \mathbb{Z}_6.$

Published on 25 Mar 2026 - 17:39

score 109 · Answer 2 · 2023-04-17 11:01:16

109

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Find the presentation for the kernel of a map from $G=\langle a,b,c\mid aba=bab,bc=cb\rangle$ to $\mathbb{Z}$.

Published on 17 Apr 2023 - 11:01

score 132 · Answer 3 · 2023-04-26 18:05:36

132

Views

Prove that the group $G = \langle x, y \, \mid \, x^2=y^3=(xy)^3=1 \rangle$ is finite.

Published on 26 Apr 2023 - 18:05

score 70 · Answer 4 · 2023-04-28 00:03:45

70

Views

Let $\Bbb Z\Bbb Z=\langle a,b\rangle$ and $N=\{waba^{-1}b^{-1}w^{-1}:w\in\Bbb Z\Bbb Z\}.$ Prove $\langle a,b\rangle/N$ is abelian

Published on 28 Apr 2023 - 0:03

score 139 · Answer 5 · 2023-04-30 15:46:53

139

Views

Rank of free groups

Published on 30 Apr 2023 - 15:46

score 81 · Answer 6 · 2023-05-04 13:59:37

81

Views

The abelianization of $\langle t_1,...,t_n | t_1^2...t_n^2 \rangle$ is $\mathbb{Z}^{n-1} \oplus \mathbb{Z}/2\mathbb{Z}$

Published on 04 May 2023 - 13:59

score 46 · Answer 7 · 2023-05-11 03:44:27

46

Views

Order of the group $\langle x, y \mid x^3 = y^2 = (xy)^3 = 1\rangle$.

Published on 11 May 2023 - 3:44

score 158 · Answer 8 · 2023-05-12 10:01:43

158

Views

Has the homology of the Baumslag Solitar groups B(1,k) been computed?

Published on 12 May 2023 - 10:01

score 71 · Answer 9 · 2026-03-25 17:42:21

71

Views

Are the only finite orders of elements of this group in $\{p^k\mid k\in\Bbb N\cup\{0\}\}?$

Published on 25 Mar 2026 - 17:42

score 85 · Answer 10 · 2023-05-17 13:55:11

85

Views

Writing down a finite axiomatization of a group given by finite presentation

Published on 17 May 2023 - 13:55

score 164 · Answer 11 · 2023-05-18 11:41:57

164

Views

Determining whether two groups are isomorphic based on Wirtinger presentation

Published on 18 May 2023 - 11:41

score 120 · Answer 12 · 2023-05-19 13:41:39

120

Views

Normal subgroup of fundamental group of Klein Bottle

Published on 19 May 2023 - 13:41

score 61 · Answer 13 · 2026-03-25 09:28:13

61

Views

Equivalence of two presentations for a quotient of the braid group

Published on 25 Mar 2026 - 9:28

score 107 · Answer 14 · 2026-03-25 19:05:02

107

Views

What is the free product with amalgamation with the trivial group?

Published on 25 Mar 2026 - 19:05

score 89 · Answer 15 · 2023-06-07 14:56:32

89

Views

Does the symmetric group S3 and the quaternion group admit a complete mapping?

Published on 07 Jun 2023 - 14:56

List Question

Computation of Amalgamated Product $\mathbb{Z}_4 \ast_{\mathbb{Z}_2} \mathbb{Z}_6.$

Find the presentation for the kernel of a map from $G=\langle a,b,c\mid aba=bab,bc=cb\rangle$ to $\mathbb{Z}$.

Prove that the group $G = \langle x, y \, \mid \, x^2=y^3=(xy)^3=1 \rangle$ is finite.

Let $\Bbb Z\Bbb Z=\langle a,b\rangle$ and $N=\{waba^{-1}b^{-1}w^{-1}:w\in\Bbb Z\Bbb Z\}.$ Prove $\langle a,b\rangle/N$ is abelian

Rank of free groups

The abelianization of $\langle t_1,...,t_n | t_1^2...t_n^2 \rangle$ is $\mathbb{Z}^{n-1} \oplus \mathbb{Z}/2\mathbb{Z}$

Order of the group $\langle x, y \mid x^3 = y^2 = (xy)^3 = 1\rangle$.

Has the homology of the Baumslag Solitar groups B(1,k) been computed?

Are the only finite orders of elements of this group in $\{p^k\mid k\in\Bbb N\cup\{0\}\}?$

Writing down a finite axiomatization of a group given by finite presentation

Determining whether two groups are isomorphic based on Wirtinger presentation

Normal subgroup of fundamental group of Klein Bottle

Equivalence of two presentations for a quotient of the braid group

What is the free product with amalgamation with the trivial group?

Does the symmetric group S3 and the quaternion group admit a complete mapping?

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