Question

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

score 126 · Answer 1 · 2020-04-11 15:46:29

126

Views

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

Published on 11 Apr 2020 - 15:46

score 302 · Answer 2 · 2026-02-23 08:32:40

302

Views

How can the following lemma be used to solve the conjugacy problem for hyperbolic groups?

Published on 23 Feb 2026 - 8:32

score 322 · Answer 3 · 2020-04-21 19:07:00

322

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 21 Apr 2020 - 19:07

score 164 · Answer 4 · 2020-04-22 05:09:49

164

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 22 Apr 2020 - 5:09

score 358 · Answer 5 · 2020-04-24 15:26:59

358

Views

Products in the free group are associative

Published on 24 Apr 2020 - 15:26

score 76 · Answer 6 · 2020-04-25 09:32:34

76

Views

Order of a Presentation related to the Quaternions

Published on 25 Apr 2020 - 9:32

score 51 · Answer 7 · 2026-03-25 11:02:24

51

Views

Is the system of subgroups whose quotient is finitely generated, an inverse system?

Published on 25 Mar 2026 - 11:02

score 64 · Answer 8 · 2026-03-25 06:29:21

64

Views

How can I easily find character table of Sergeev group (finite)?

Published on 25 Mar 2026 - 6:29

score 187 · Answer 9 · 2020-05-10 16:04:42

187

Views

Find the group with presentation $\langle x, y: xy=yx, x^5=y^3\rangle$.

Published on 10 May 2020 - 16:04

score 379 · Answer 10 · 2020-05-12 15:44:25

379

Views

Intuition of recursively presented groups

Published on 12 May 2020 - 15:44

score 569 · Answer 11 · 2026-03-24 22:01:46

569

Views

Exponential Growth and Decay Model for Human Genealogy (Common Ancestor)

Published on 24 Mar 2026 - 22:01

score 150 · Answer 12 · 2020-05-17 19:25:07

150

Views

Show that there is an injective homomorphism from $G_2 = \langle a, b \mid aba^{-1}b^{-1}\rangle$ to $G_1 = \langle x, y \mid xyx^{-1}y\rangle$.

Published on 17 May 2020 - 19:25

score 84 · Answer 13 · 2020-05-18 07:22:45

84

Views

How to show the elements ${x^p}$ and $y$ are commute based on relation ${x^y}={x^{1+p}}$

Published on 18 May 2020 - 7:22

score 244 · Answer 14 · 2020-05-18 19:05:35

244

Views

Finding the group order from the presentation of a group and deciding if it is abelian

Published on 18 May 2020 - 19:05

score 250 · Answer 15 · 2020-05-20 16:41:18

250

Views

Normal subgroups from generators

Published on 20 May 2020 - 16:41

List Question

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

How can the following lemma be used to solve the conjugacy problem for hyperbolic groups?

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.

Products in the free group are associative

Order of a Presentation related to the Quaternions

Is the system of subgroups whose quotient is finitely generated, an inverse system?

How can I easily find character table of Sergeev group (finite)?

Find the group with presentation $\langle x, y: xy=yx, x^5=y^3\rangle$.

Intuition of recursively presented groups

Exponential Growth and Decay Model for Human Genealogy (Common Ancestor)

Show that there is an injective homomorphism from $G_2 = \langle a, b \mid aba^{-1}b^{-1}\rangle$ to $G_1 = \langle x, y \mid xyx^{-1}y\rangle$.

How to show the elements ${x^p}$ and $y$ are commute based on relation ${x^y}={x^{1+p}}$

Finding the group order from the presentation of a group and deciding if it is abelian

Normal subgroups from generators

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