Question

Let $G=\langle(1,2,3),(1,2)(4,5,6,7)\rangle.$ Find the center of $G$ using a presentation.

score 65 · Answer 1 · 2020-03-08 05:31:43

65

Views

Let $G=\langle(1,2,3),(1,2)(4,5,6,7)\rangle.$ Find the center of $G$ using a presentation.

Published on 08 Mar 2020 - 5:31

score 129 · Answer 2 · 2026-03-25 21:51:07

129

Views

Let $F_n$ be free on $n$ letters and $g_1,...,g_{2m}\in F_n$. Can $F_n/⟨⟨[g_1,g_2],...,[g_{2m-1},g_{2m}]⟩⟩$ have torsion elements?

Published on 25 Mar 2026 - 21:51

score 47 · Answer 3 · 2020-03-29 02:36:16

47

Views

application of Van Kampen - Fund. groups

Published on 29 Mar 2020 - 2:36

score 121 · Answer 4 · 2026-03-25 21:50:01

121

Views

Why is $\langle S\mid R\cup R'\rangle $ a presentation for $G/N(R')$, where $G$ is a group with presentation $\langle S\mid R\rangle?$

Published on 25 Mar 2026 - 21:50

score 315 · Answer 5 · 2026-03-25 16:14:04

315

Views

Weeks Manifold - the Heegaard splitting and presentations of its fundamental group

Published on 25 Mar 2026 - 16:14

score 394 · Answer 6 · 2026-03-25 06:01:42

394

Views

How to define a finitely presented group in GAP

Published on 25 Mar 2026 - 6:01

score 70 · Answer 7 · 2020-04-09 19:04:41

70

Views

Notation for presentation of a quotient of a free group

Published on 09 Apr 2020 - 19:04

score 91 · Answer 8 · 2026-03-25 21:48:55

91

Views

Clarification regarding condition of semidirect product of cyclic groups

Published on 25 Mar 2026 - 21:48

score 34 · Answer 9 · 2020-04-10 15:30:37

34

Views

Order of cyclic group defined by presentation is finite

Published on 10 Apr 2020 - 15:30

score 127 · Answer 10 · 2026-03-25 23:10:03

127

Views

Showing $\mathbb{Z}\times\mathbb{Z}$ is isomorphic to the group $\langle x,y,|xy=yx\rangle$

Published on 25 Mar 2026 - 23:10

score 323 · Answer 11 · 2026-03-25 23:13:07

323

Views

How to show $G_{m}\cong G_n $ if and only if $n=m$, where $G_m:= \langle x,y \mid x(yx)^{m}=y(xy)^{m}\rangle$

Published on 25 Mar 2026 - 23:13

score 165 · Answer 12 · 2026-03-25 23:13:03

165

Views

Let $G=\langle x,y|x^{8}=y^{2}=e,yxyx^{3}=e \rangle$. Show that $|G|\leq16$. Assuming that $|G|=16$, find the center of $G$ and the order of xy.

Published on 25 Mar 2026 - 23:13

score 200 · Answer 13 · 2020-04-23 17:57:29

200

Views

Induced Group Representation

Published on 23 Apr 2020 - 17:57

score 77 · Answer 14 · 2026-03-25 23:10:11

77

Views

Order of a Presentation related to the Quaternions

Published on 25 Mar 2026 - 23:10

score 178 · Answer 15 · 2020-04-30 18:00:45

178

Views

Is the presentation of the generalized quaternion group of order 16 on Groupprops wrong, or am I missing something?

Published on 30 Apr 2020 - 18:00

List Question

Let $G=\langle(1,2,3),(1,2)(4,5,6,7)\rangle.$ Find the center of $G$ using a presentation.

Let $F_n$ be free on $n$ letters and $g_1,...,g_{2m}\in F_n$. Can $F_n/⟨⟨[g_1,g_2],...,[g_{2m-1},g_{2m}]⟩⟩$ have torsion elements?

application of Van Kampen - Fund. groups

Why is $\langle S\mid R\cup R'\rangle $ a presentation for $G/N(R')$, where $G$ is a group with presentation $\langle S\mid R\rangle?$

Weeks Manifold - the Heegaard splitting and presentations of its fundamental group

How to define a finitely presented group in GAP

Notation for presentation of a quotient of a free group

Clarification regarding condition of semidirect product of cyclic groups

Order of cyclic group defined by presentation is finite

Showing $\mathbb{Z}\times\mathbb{Z}$ is isomorphic to the group $\langle x,y,|xy=yx\rangle$

How to show $G_{m}\cong G_n $ if and only if $n=m$, where $G_m:= \langle x,y \mid x(yx)^{m}=y(xy)^{m}\rangle$

Let $G=\langle x,y|x^{8}=y^{2}=e,yxyx^{3}=e \rangle$. Show that $|G|\leq16$. Assuming that $|G|=16$, find the center of $G$ and the order of xy.

Induced Group Representation

Order of a Presentation related to the Quaternions

Is the presentation of the generalized quaternion group of order 16 on Groupprops wrong, or am I missing something?

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