Question

If an infinite group $G$ is generated by two elements $a,b$ such that $a^n=b^n=e$, must $x^n=e$ have infinitely many solutions?

score 182 · Answer 1 · 2023-08-27 00:41:24

182

Views

If an infinite group $G$ is generated by two elements $a,b$ such that $a^n=b^n=e$, must $x^n=e$ have infinitely many solutions?

Published on 27 Aug 2023 - 0:41

score 83 · Answer 2 · 2023-08-28 18:16:17

83

Views

Using the Orbit-Stabiliser Theorem to prove a set of matrices is a subgroup of $\operatorname{GL}_2(\mathbb{R})$

Published on 28 Aug 2023 - 18:16

score 469 · Answer 3 · 2023-09-12 11:24:47

469

Views

Has every infinite simple group a faithful irreducible representation?

Published on 12 Sep 2023 - 11:24

score 386 · Answer 4 · 2023-10-04 16:34:36

386

Views

What is the cardinality of the set of all groups (up to isomorphism) of countable order?

Published on 04 Oct 2023 - 16:34

score 108 · Answer 5 · 2026-03-25 19:00:49

108

Views

Proving certain triangle groups are infinite

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score 102 · Answer 6 · 2023-11-01 13:12:26

102

Views

Infinite non cyclic group with proper subgroups being cyclic

Published on 01 Nov 2023 - 13:12

score 51 · Answer 7 · 2023-11-05 07:10:38

51

Views

Comparing cardinality of set of real numbers $[2,3]$ and set of real numbers $[4,5]$

Published on 05 Nov 2023 - 7:10

score 54 · Answer 8 · 2023-12-04 21:52:21

54

Views

If every proper subgroup of an infinite group $G$ is cyclic, then $G$ is abelian

Published on 04 Dec 2023 - 21:52

score 79 · Answer 9 · 2026-03-25 16:03:43

79

Views

Non-nilpotent group where the union of the upper central groups equals the whole group

Published on 25 Mar 2026 - 16:03

score 216 · Answer 10 · 2026-03-25 16:01:24

216

Views

Finitely generated, nilpotent, torsion-free group that is also radicable

Published on 25 Mar 2026 - 16:01

score 62 · Answer 11 · 2024-01-21 22:18:55

62

Views

Doubling radii of balls in groups of polynomial growth

Published on 21 Jan 2024 - 22:18

score 55 · Answer 12 · 2024-01-25 23:42:03

55

Views

Let $K\le H\le G$ with $[G:H]<\infty$. Is $[G:K]<\infty$ necessarily?

Published on 25 Jan 2024 - 23:42

score 41 · Answer 13 · 2026-03-26 08:04:32

41

Views

Subgroups and Quotient Groups of Infinite bounded Abelian p-groups

Published on 26 Mar 2026 - 8:04

score 34 · Answer 14 · 2024-03-04 07:23:57

34

Views

How to Prove the Divergence of an Improper Integral Involving Absolute Value

Published on 04 Mar 2024 - 7:23

score 76 · Answer 15 · 2026-02-23 05:50:32

76

Views

Non-abelian groups with trivial socle.

Published on 23 Feb 2026 - 5:50

List Question

If an infinite group $G$ is generated by two elements $a,b$ such that $a^n=b^n=e$, must $x^n=e$ have infinitely many solutions?

Using the Orbit-Stabiliser Theorem to prove a set of matrices is a subgroup of $\operatorname{GL}_2(\mathbb{R})$

Has every infinite simple group a faithful irreducible representation?

What is the cardinality of the set of all groups (up to isomorphism) of countable order?

Proving certain triangle groups are infinite

Infinite non cyclic group with proper subgroups being cyclic

Comparing cardinality of set of real numbers $[2,3]$ and set of real numbers $[4,5]$

If every proper subgroup of an infinite group $G$ is cyclic, then $G$ is abelian

Non-nilpotent group where the union of the upper central groups equals the whole group

Finitely generated, nilpotent, torsion-free group that is also radicable

Doubling radii of balls in groups of polynomial growth

Let $K\le H\le G$ with $[G:H]<\infty$. Is $[G:K]<\infty$ necessarily?

Subgroups and Quotient Groups of Infinite bounded Abelian p-groups

How to Prove the Divergence of an Improper Integral Involving Absolute Value

Non-abelian groups with trivial socle.

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