Question

Why doesn't the infinite dihedral group contain a free subgroup of rank 2?

score 161 · Answer 1 · 2026-03-25 19:10:28

161

Views

Why doesn't the infinite dihedral group contain a free subgroup of rank 2?

Published on 25 Mar 2026 - 19:10

score 45 · Answer 2 · 2023-06-11 00:01:19

45

Views

Question about group of rank Aleph-Null.

Published on 11 Jun 2023 - 0:01

score 62 · Answer 3 · 2026-03-26 19:18:48

62

Views

Recovering an element of a free group from its projections

Published on 26 Mar 2026 - 19:18

score 36 · Answer 4 · 2023-06-18 11:20:18

36

Views

Let $H ≤ F_A$ be finitely generated and $g \in F_A$. Show that it is decidable if $xgx^{-1} \in H$ for some $x \in F_A$

Published on 18 Jun 2023 - 11:20

score 109 · Answer 5 · 2023-06-20 21:09:25

109

Views

A subgroup $H$ of an abelian group $G$ is a direct summand iff $G/H$ is free?

Published on 20 Jun 2023 - 21:09

score 197 · Answer 6 · 2026-03-26 09:26:20

197

Views

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

Published on 26 Mar 2026 - 9:26

score 64 · Answer 7 · 2023-07-06 15:12:52

64

Views

Understanding why this "obvious" approach to Schreier-Nielsen's theorem doesn't work

Published on 06 Jul 2023 - 15:12

score 90 · Answer 8 · 2023-07-11 14:58:34

90

Views

Questions to limit groups (over free groups)

Published on 11 Jul 2023 - 14:58

score 32 · Answer 9 · 2026-03-26 12:50:38

32

Views

$\prod_p \mathbb{Z}/p\mathbb{Z}$ is not the direct sum of $\bigoplus_p \mathbb{Z}/p\mathbb{Z}$ and a torsion-free subgroup

Published on 26 Mar 2026 - 12:50

score 66 · Answer 10 · 2023-07-14 13:46:35

66

Views

Computing $\mathrm{Fix}(\phi)$ for autormophisms $\phi$ of free groups

Published on 14 Jul 2023 - 13:46

score 144 · Answer 11 · 2026-03-26 09:18:08

144

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 26 Mar 2026 - 9:18

score 123 · Answer 12 · 2023-07-20 13:28:26

123

Views

A group generated by two elements with uncountably many normal subgroups

Published on 20 Jul 2023 - 13:28

score 85 · Answer 13 · 2023-07-28 19:20:00

85

Views

Free product of finite groups that is outside graph theory

Published on 28 Jul 2023 - 19:20

score 68 · Answer 14 · 2023-08-01 19:08:55

68

Views

Are any quotients of braid groups non-trivial free products?

Published on 01 Aug 2023 - 19:08

score 95 · Answer 15 · 2026-03-25 06:04:04

95

Views

Mapping class group of surfaces, free products, and trees

Published on 25 Mar 2026 - 6:04

List Question

Why doesn't the infinite dihedral group contain a free subgroup of rank 2?

Question about group of rank Aleph-Null.

Recovering an element of a free group from its projections

Let $H ≤ F_A$ be finitely generated and $g \in F_A$. Show that it is decidable if $xgx^{-1} \in H$ for some $x \in F_A$

A subgroup $H$ of an abelian group $G$ is a direct summand iff $G/H$ is free?

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

Understanding why this "obvious" approach to Schreier-Nielsen's theorem doesn't work

Questions to limit groups (over free groups)

$\prod_p \mathbb{Z}/p\mathbb{Z}$ is not the direct sum of $\bigoplus_p \mathbb{Z}/p\mathbb{Z}$ and a torsion-free subgroup

Computing $\mathrm{Fix}(\phi)$ for autormophisms $\phi$ of free groups

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 $G = \langle S \rangle$

A group generated by two elements with uncountably many normal subgroups

Free product of finite groups that is outside graph theory

Are any quotients of braid groups non-trivial free products?

Mapping class group of surfaces, free products, and trees

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