List questions from free-groups

Published on 03 Dec 2021 - 14:29

293

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Every element in a free group is conjugate to a cyclically reduced word

Published on 27 Mar 2026 - 22:55

76

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Problem handling free groups in algebraic topology

Published on 27 Dec 2021 - 20:24

139

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Rotman's Algebraic Topology Lemma 9.11

Published on 04 Jan 2022 - 11:23

137

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Describe all path-connected $3$ fold covers of $X=S^1 \vee \mathbb{R}P^2$

Published on 11 Jan 2022 - 2:48

143

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Show that the kernel of a homomorphism from $G_1*G_2$ to $G_1\times G_2$ is free on $S$

Published on 13 Jan 2022 - 21:01

222

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A certain free product of groups is virtually torsion-free

Published on 26 Mar 2026 - 4:34

70

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Question about f.g. normal subgroups of f.g. free groups

Published on 25 Jan 2022 - 17:48

136

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Find rank of subgroup of $F_2 = \langle x,y\rangle$ generated by $xyx^{-1}y, yxy^{-1}x$.

Published on 26 Jan 2022 - 18:27

58

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On the meaning of "$F^2$" in Robinson's Exercise 6.1.7.

Published on 28 Jan 2022 - 23:41

56

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Order of a quotient of a free abelian group

Published on 27 Mar 2026 - 5:03

186

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A group is locally free exactly when its finitely generated subgroups are free

Published on 31 Jan 2022 - 13:37

157

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Construction of a free group

Published on 31 Jan 2022 - 22:38

76

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Free left $R$-module can be endowed with $(R,R)$-bimodule structure. Basis-dependent definition?

Published on 25 Mar 2026 - 9:26

79

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If $X$ is an infinite set, then $|X|=|F(X)|$, where $F(X)$ is the free group on $X$

Published on 28 Mar 2026 - 6:00

List Question

Torus is the only closed orientable surface regularly covered by punctured plane

Every element in a free group is conjugate to a cyclically reduced word

Problem handling free groups in algebraic topology

Rotman's Algebraic Topology Lemma 9.11

Describe all path-connected $3$ fold covers of $X=S^1 \vee \mathbb{R}P^2$

Show that the kernel of a homomorphism from $G_1*G_2$ to $G_1\times G_2$ is free on $S$

A certain free product of groups is virtually torsion-free

Question about f.g. normal subgroups of f.g. free groups

Find rank of subgroup of $F_2 = \langle x,y\rangle$ generated by $xyx^{-1}y, yxy^{-1}x$.

On the meaning of "$F^2$" in Robinson's Exercise 6.1.7.

Order of a quotient of a free abelian group

A group is locally free exactly when its finitely generated subgroups are free

Construction of a free group

Free left $R$-module can be endowed with $(R,R)$-bimodule structure. Basis-dependent definition?

If $X$ is an infinite set, then $|X|=|F(X)|$, where $F(X)$ is the free group on $X$

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