Question

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

score 108 · Answer 1 · 2020-02-25 02:57:34

108

Views

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

Published on 25 Feb 2020 - 2:57

score 39 · Answer 2 · 2026-02-23 05:17:16

39

Views

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

Published on 23 Feb 2026 - 5:17

score 201 · Answer 3 · 2020-03-06 01:05:38

201

Views

A group word having no trivial proper subword

Published on 06 Mar 2020 - 1:05

score 738 · Answer 4 · 2026-03-25 16:13:58

738

Views

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

Published on 25 Mar 2026 - 16:13

score 233 · Answer 5 · 2026-03-25 09:29:50

233

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 25 Mar 2026 - 9:29

score 42 · Answer 6 · 2020-03-17 23:37:12

42

Views

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

Published on 17 Mar 2020 - 23:37

score 321 · Answer 7 · 2020-03-23 09:35:37

321

Views

Probability of a group being finite

Published on 23 Mar 2020 - 9:35

score 128 · Answer 8 · 2020-03-25 00:00:33

128

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 25 Mar 2020 - 0:00

score 63 · Answer 9 · 2026-03-25 11:10:12

63

Views

Colorings versus geometric group theory method

Published on 25 Mar 2026 - 11:10

score 383 · Answer 10 · 2026-03-25 12:50:43

383

Views

Are all almost virtually free groups word hyperbolic?

Published on 25 Mar 2026 - 12:50

score 120 · Answer 11 · 2020-04-02 16:03:51

120

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 02 Apr 2020 - 16:03

score 394 · Answer 12 · 2026-03-25 06:01:42

394

Views

How to define a finitely presented group in GAP

Published on 25 Mar 2026 - 6:01

score 45 · Answer 13 · 2020-04-08 22:35:59

45

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 08 Apr 2020 - 22:35

score 195 · Answer 14 · 2020-04-09 20:34:31

195

Views

When is a quotient group of a free group finite?

Published on 09 Apr 2020 - 20:34

score 90 · Answer 15 · 2020-04-10 11:09:54

90

Views

Clarification regarding condition of semidirect product of cyclic groups

Published on 10 Apr 2020 - 11:09

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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