Question

Finitely generated group unlikely to be generated by randomly chosen elements.

score 109 · Answer 1 · 2026-03-25 21:46:18

109

Views

Finitely generated group unlikely to be generated by randomly chosen elements.

Published on 25 Mar 2026 - 21:46

score 40 · Answer 2 · 2026-04-09 09:29:57

40

Views

Why can a group act with left action on a function in polya counting?

Published on 09 Apr 2026 - 9:29

score 203 · Answer 3 · 2026-05-10 16:16:36

203

Views

A group word having no trivial proper subword

Published on 10 May 2026 - 16:16

score 741 · Answer 4 · 2026-05-10 17:01:16

741

Views

Can a Free product with amalgamation of $\mathbb{Z}*\mathbb{Z}$ be isomorphic to $\mathbb{Z}\times \mathbb{Z}$?

Published on 10 May 2026 - 17:01

score 234 · Answer 5 · 2026-05-10 17:39:16

234

Views

Let $w_0$ be the element of longest length in a Coxeter group. Show that $l(w_0w)=l(ww_0)=l(w_0)-l(w)$? Find $w_0$ explicitly in $S_n$.

Published on 10 May 2026 - 17:39

score 43 · Answer 6 · 2026-03-25 21:50:03

43

Views

If $g_i$ generate $G$, then $x^kg_i^\pm x^{-k}$ generate $[G,G]$

Published on 25 Mar 2026 - 21:50

score 323 · Answer 7 · 2026-05-11 06:39:48

323

Views

Probability of a group being finite

Published on 11 May 2026 - 6:39

score 130 · Answer 8 · 2026-05-11 02:50:16

130

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 11 May 2026 - 2:50

score 64 · Answer 9 · 2026-05-11 01:23:11

64

Views

Colorings versus geometric group theory method

Published on 11 May 2026 - 1:23

score 385 · Answer 10 · 2026-05-10 15:08:20

385

Views

Are all almost virtually free groups word hyperbolic?

Published on 10 May 2026 - 15:08

score 121 · Answer 11 · 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 395 · Answer 12 · 2026-05-10 19:08:14

395

Views

How to define a finitely presented group in GAP

Published on 10 May 2026 - 19:08

score 46 · Answer 13 · 2026-03-25 21:54:03

46

Views

Given a group $G$ of order $6$ and $a,b\in G$ with $|a|=3$ and $|b|=2$, show that the elements of $G$ are unique.

Published on 25 Mar 2026 - 21:54

score 196 · Answer 14 · 2026-03-25 21:49:43

196

Views

When is a quotient group of a free group finite?

Published on 25 Mar 2026 - 21:49

score 93 · Answer 15 · 2026-04-14 09:40:45

93

Views

Clarification regarding condition of semidirect product of cyclic groups

Published on 14 Apr 2026 - 9:40

List Question

Finitely generated group unlikely to be generated by randomly chosen elements.

Why can a group act with left action on a function in polya counting?

A group word having no trivial proper subword

Can a Free product with amalgamation of $\mathbb{Z}*\mathbb{Z}$ be isomorphic to $\mathbb{Z}\times \mathbb{Z}$?

Let $w_0$ be the element of longest length in a Coxeter group. Show that $l(w_0w)=l(ww_0)=l(w_0)-l(w)$? Find $w_0$ explicitly in $S_n$.

If $g_i$ generate $G$, then $x^kg_i^\pm x^{-k}$ generate $[G,G]$

Probability of a group being finite

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?

Colorings versus geometric group theory method

Are all almost virtually free groups word hyperbolic?

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

How to define a finitely presented group in GAP

Given a group $G$ of order $6$ and $a,b\in G$ with $|a|=3$ and $|b|=2$, show that the elements of $G$ are unique.

When is a quotient group of a free group finite?

Clarification regarding condition of semidirect product of cyclic groups

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