Question

Does a presentation of a group correspond to a unique group?

score 125 · Answer 1 · 2023-06-08 02:14:40

125

Views

Does a presentation of a group correspond to a unique group?

Published on 08 Jun 2023 - 2:14

score 62 · Answer 2 · 2023-06-09 22:52:59

62

Views

If $\forall n\in\Bbb N$, if $g\in G$ with $|g|=n$ implies $\forall m\in\Bbb N,\exists h_m\in G,|h_m|=n^m,$ then can non-torsion-free $G$ be f.p.?

Published on 09 Jun 2023 - 22:52

score 74 · Answer 3 · 2023-06-14 23:36:13

74

Views

Presentation of Klein group: Show $G=\langle a,b\mid a^2,b^2,(ab)^2,(ba)^2,ab^2a\rangle$ is iso to $K_4=\langle x,y\mid x^2,y^2,xyx^{-1}y^{-1}\rangle$

Published on 14 Jun 2023 - 23:36

score 122 · Answer 4 · 2023-06-19 17:37:16

122

Views

When can we say $H$ is a subgroup of $G$ given their presentations?

Published on 19 Jun 2023 - 17:37

score 96 · Answer 5 · 2026-03-25 17:43:40

96

Views

Why isn't a coxeter group a HNN-extension?

Published on 25 Mar 2026 - 17:43

score 125 · Answer 6 · 2023-06-29 03:13:31

125

Views

Number of Distinct Words of arbitrary length $k$ in Euclidean N-Space (i.e; $\mathbb{Z}^N$)

Published on 29 Jun 2023 - 3:13

score 196 · Answer 7 · 2023-07-04 00:49:08

196

Views

Is $\Bbb Z^3$ a one-relator group?

Published on 04 Jul 2023 - 0:49

score 174 · Answer 8 · 2026-03-26 06:20:30

174

Views

Can two non-isomorphic groups have the same Cayley graphs?

Published on 26 Mar 2026 - 6:20

score 143 · Answer 9 · 2023-07-19 20:27:03

143

Views

If $a^{p_1} b^{q_1}\ldots a^{p_n} b^{q_n} = e$ then $S = \{a,b\}$ is not a free generating set of $G = \langle S \rangle$

Published on 19 Jul 2023 - 20:27

score 108 · Answer 10 · 2026-03-25 15:58:15

108

Views

Proving that this relation implies another relation on the Coxeter group [4,3,3,4].

Published on 25 Mar 2026 - 15:58

score 57 · Answer 11 · 2026-02-23 13:37:48

57

Views

Is the Baumslag Solitair group B(2,3) really non-Hopfian?

Published on 23 Feb 2026 - 13:37

score 61 · Answer 12 · 2023-08-01 14:19:37

61

Views

Show that every automorphism of $F_{20} = \langle a, b \mid a^5 = b^4 = 1, bab^{-1} = a^3\rangle $ is an inner automorphism

Published on 01 Aug 2023 - 14:19

score 489 · Answer 13 · 2023-08-02 04:59:22

489

Views

Show, using presentations, that $\Bbb Z_m\times\Bbb Z_n\cong\Bbb Z_{{\rm lcm}(m,n)}\times \Bbb Z_{\gcd(m,n)} .$

Published on 02 Aug 2023 - 4:59

score 57 · Answer 14 · 2023-08-04 18:00:44

57

Views

Can the growth of a group be bounded concretely when the group is of subexponential growth?

Published on 04 Aug 2023 - 18:00

score 136 · Answer 15 · 2023-08-08 03:47:51

136

Views

Show that $G = \langle a,b \mid a^2b = ba^3\rangle$ is nonabelian.

Published on 08 Aug 2023 - 3:47

List Question

Does a presentation of a group correspond to a unique group?

If $\forall n\in\Bbb N$, if $g\in G$ with $|g|=n$ implies $\forall m\in\Bbb N,\exists h_m\in G,|h_m|=n^m,$ then can non-torsion-free $G$ be f.p.?

Presentation of Klein group: Show $G=\langle a,b\mid a^2,b^2,(ab)^2,(ba)^2,ab^2a\rangle$ is iso to $K_4=\langle x,y\mid x^2,y^2,xyx^{-1}y^{-1}\rangle$

When can we say $H$ is a subgroup of $G$ given their presentations?

Why isn't a coxeter group a HNN-extension?

Number of Distinct Words of arbitrary length $k$ in Euclidean N-Space (i.e; $\mathbb{Z}^N$)

Is $\Bbb Z^3$ a one-relator group?

Can two non-isomorphic groups have the same Cayley graphs?

If $a^{p_1} b^{q_1}\ldots a^{p_n} b^{q_n} = e$ then $S = \{a,b\}$ is not a free generating set of $G = \langle S \rangle$

Proving that this relation implies another relation on the Coxeter group [4,3,3,4].

Is the Baumslag Solitair group B(2,3) really non-Hopfian?

Show that every automorphism of $F_{20} = \langle a, b \mid a^5 = b^4 = 1, bab^{-1} = a^3\rangle $ is an inner automorphism

Show, using presentations, that $\Bbb Z_m\times\Bbb Z_n\cong\Bbb Z_{{\rm lcm}(m,n)}\times \Bbb Z_{\gcd(m,n)} .$

Can the growth of a group be bounded concretely when the group is of subexponential growth?

Show that $G = \langle a,b \mid a^2b = ba^3\rangle$ is nonabelian.

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