Question

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

score 158 · Answer 1 · 2019-12-29 09:42:52

158

Views

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

Published on 29 Dec 2019 - 9:42

score 32 · Answer 2 · 2019-12-29 13:32:32

32

Views

Can the context-sensitivity of word problem in group $G$ be equivalently characterised through some structural properties of $G$?

Published on 29 Dec 2019 - 13:32

score 38 · Answer 3 · 2019-12-30 18:14:30

38

Views

Do there exist such groups $G$, such that $L(G, A)$ is context-free, but $(A \cup A^{-1})^* \setminus L(G, A)$ isn't?

Published on 30 Dec 2019 - 18:14

score 55 · Answer 4 · 2019-12-31 10:19:35

55

Views

Do there exist such groups $G$, such that $(A \cup A^{-1})^* \setminus L(G, A)$ is recursively enumerable, but $L(G, A)$ isn't?

Published on 31 Dec 2019 - 10:19

score 63 · Answer 5 · 2026-03-25 09:28:25

63

Views

Coxeter graph of the group $\mathbb{Z}_2 \times \mathbb{Z}_2 \times \dots \times \mathbb{Z}_2$

Published on 25 Mar 2026 - 9:28

score 202 · Answer 6 · 2020-01-06 23:44:36

202

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 06 Jan 2020 - 23:44

score 95 · Answer 7 · 2020-01-08 11:39:45

95

Views

Finding all the elements of a group

Published on 08 Jan 2020 - 11:39

score 1.5k · Answer 8 · 2020-01-09 20:32:21

1.5k

Views

A presentation of the infinite dihedral group.

Published on 09 Jan 2020 - 20:32

score 623 · Answer 9 · 2020-01-10 21:28:16

623

Views

Presentation $\langle x,y \mid x^3=y^3=(xy)^3=1\rangle\cong\langle t\rangle\ltimes A$

Published on 10 Jan 2020 - 21:28

score 398 · Answer 10 · 2020-01-12 02:31:47

398

Views

Showing $\langle x,y\mid x^p=y^p=(xy)^p=1\rangle$ is infinite if $p>2, p$ prime.

Published on 12 Jan 2020 - 2:31

score 150 · Answer 11 · 2020-01-12 20:06:38

150

Views

Presentations: fewer relations than generators implies $G$ infinite.

Published on 12 Jan 2020 - 20:06

score 324 · Answer 12 · 2020-01-13 03:06:36

324

Views

When can you replace the generators of a group with conjugates?

Published on 13 Jan 2020 - 3:06

score 124 · Answer 13 · 2020-01-14 02:53:09

124

Views

Are all groups with relators whose exponents sum to $0$ totally orderable?

Published on 14 Jan 2020 - 2:53

score 440 · Answer 14 · 2020-01-14 21:41:08

440

Views

Suppose that $G$ is a group with $n$ generators and $r$ relations whether $r < n$. Prove that $G$ is infinite.

Published on 14 Jan 2020 - 21:41

score 64 · Answer 15 · 2020-01-15 14:06:03

64

Views

Presentations, automorphisms and natural homomorphisms.

Published on 15 Jan 2020 - 14:06

List Question

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

Can the context-sensitivity of word problem in group $G$ be equivalently characterised through some structural properties of $G$?

Do there exist such groups $G$, such that $L(G, A)$ is context-free, but $(A \cup A^{-1})^* \setminus L(G, A)$ isn't?

Do there exist such groups $G$, such that $(A \cup A^{-1})^* \setminus L(G, A)$ is recursively enumerable, but $L(G, A)$ isn't?

Coxeter graph of the group $\mathbb{Z}_2 \times \mathbb{Z}_2 \times \dots \times \mathbb{Z}_2$

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

Finding all the elements of a group

A presentation of the infinite dihedral group.

Presentation $\langle x,y \mid x^3=y^3=(xy)^3=1\rangle\cong\langle t\rangle\ltimes A$

Showing $\langle x,y\mid x^p=y^p=(xy)^p=1\rangle$ is infinite if $p>2, p$ prime.

Presentations: fewer relations than generators implies $G$ infinite.

When can you replace the generators of a group with conjugates?

Are all groups with relators whose exponents sum to $0$ totally orderable?

Suppose that $G$ is a group with $n$ generators and $r$ relations whether $r < n$. Prove that $G$ is infinite.

Presentations, automorphisms and natural homomorphisms.

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