Question

Can any relation in the group be derived from the relations in the presentation?

score 163 · Answer 1 · 2026-03-25 17:22:52

163

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Can any relation in the group be derived from the relations in the presentation?

Published on 25 Mar 2026 - 17:22

score 216 · Answer 2 · 2026-03-25 17:26:58

216

Views

Show $\langle x,y|x^3=y^3=(xy)^3=1\rangle$ is isomophic to $A\rtimes\langle t\rangle$, where $t^3=1$ and $A=\langle a\rangle\times\langle b\rangle$.

Published on 25 Mar 2026 - 17:26

score 208 · Answer 3 · 2019-12-03 07:04:05

208

Views

Group with a given presentation, finite or infinite?

Published on 03 Dec 2019 - 7:04

score 117 · Answer 4 · 2026-03-25 20:15:17

117

Views

Showing Isomorphism between Semi direct product $C_7 \rtimes C_3$ and presentation G

Published on 25 Mar 2026 - 20:15

score 188 · Answer 5 · 2019-12-14 00:13:00

188

Views

Group Theory: Proving that a presentation describes a known group

Published on 14 Dec 2019 - 0:13

score 107 · Answer 6 · 2026-03-25 17:22:20

107

Views

Effect of Generators and Relations on a Finite Group's Order

Published on 25 Mar 2026 - 17:22

score 53 · Answer 7 · 2019-12-14 17:22:25

53

Views

How can I show that two groups represented by permutation are different?

Published on 14 Dec 2019 - 17:22

score 119 · Answer 8 · 2019-12-18 16:17:37

119

Views

Conditions to check for homomorphism described on generators and relations

Published on 18 Dec 2019 - 16:17

score 53 · Answer 9 · 2019-12-23 10:58:56

53

Views

Is this a presentation of a known group?

Published on 23 Dec 2019 - 10:58

score 110 · Answer 10 · 2026-03-25 17:26:10

110

Views

Can Higman's embedding theorem be generalised that way?

Published on 25 Mar 2026 - 17:26

score 159 · Answer 11 · 2026-03-25 18:55:38

159

Views

An example of group which is regularly presented, but not finitely presented

Published on 25 Mar 2026 - 18:55

score 305 · Answer 12 · 2019-12-29 20:40:41

305

Views

Finding a finite presentation for the kernel of a homomorphism

Published on 29 Dec 2019 - 20:40

score 146 · Answer 13 · 2020-01-06 23:33:01

146

Views

Presentation $\langle x,y\mid x^3=y^3=(xy)^3=1\rangle $ with normal abelian subgroup.

Published on 06 Jan 2020 - 23:33

score 203 · Answer 14 · 2026-03-25 18:59:08

203

Views

How to approach proofs similar to "Show a group, $G$, is infinite if $G = \langle r, s, t\mid rst = 1\rangle $"

Published on 25 Mar 2026 - 18:59

score 125 · Answer 15 · 2020-01-07 13:00:22

125

Views

Showing $\langle a,b\mid ab^2＝b^3a, ba^2＝a^3\rangle$ is isomorphic to the trivial group.

Published on 07 Jan 2020 - 13:00

List Question

Can any relation in the group be derived from the relations in the presentation?

Show $\langle x,y|x^3=y^3=(xy)^3=1\rangle$ is isomophic to $A\rtimes\langle t\rangle$, where $t^3=1$ and $A=\langle a\rangle\times\langle b\rangle$.

Group with a given presentation, finite or infinite?

Showing Isomorphism between Semi direct product $C_7 \rtimes C_3$ and presentation G

Group Theory: Proving that a presentation describes a known group

Effect of Generators and Relations on a Finite Group's Order

How can I show that two groups represented by permutation are different?

Conditions to check for homomorphism described on generators and relations

Is this a presentation of a known group?

Can Higman's embedding theorem be generalised that way?

An example of group which is regularly presented, but not finitely presented

Finding a finite presentation for the kernel of a homomorphism

Presentation $\langle x,y\mid x^3=y^3=(xy)^3=1\rangle $ with normal abelian subgroup.

How to approach proofs similar to "Show a group, $G$, is infinite if $G = \langle r, s, t\mid rst = 1\rangle $"

Showing $\langle a,b\mid ab^2＝b^3a, ba^2＝a^3\rangle$ is isomorphic to the trivial group.

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