Question

Intuition of characteristic property of the free group

score 294 · Answer 1 · 2026-04-13 04:10:13

294

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Intuition of characteristic property of the free group

Published on 13 Apr 2026 - 4:10

score 1.1k · Answer 2 · 2026-04-08 04:55:37

1.1k

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Understanding the free product amalgamation with an example

Published on 08 Apr 2026 - 4:55

score 92 · Answer 3 · 2026-04-09 03:50:35

92

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$\mathbb{Z}\ast\mathbb{Z}\ast\mathbb{Z}$ is an index two subgroup of $\mathbb{Z}\ast\mathbb{Z}$

Published on 09 Apr 2026 - 3:50

score 317 · Answer 4 · 2026-04-15 10:38:03

317

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Quotient of amalgamated free product by normal subgroup

Published on 15 Apr 2026 - 10:38

score 532 · Answer 5 · 2026-04-15 05:09:13

532

Views

Showing that the free group of a disjoint union is isomorphic to the free product of the corresponding free groups

Published on 15 Apr 2026 - 5:09

score 38 · Answer 6 · 2026-04-16 00:56:10

38

Views

Why does no non-trivial reduced words in $H_1 \backslash \{e\} \sqcup H_2 \backslash \{e\}$ imply that $\left< H_1, H_2 \right> = H_1 \ast H_2$?

Published on 16 Apr 2026 - 0:56

score 36 · Answer 7 · 2026-04-09 23:30:59

36

Views

Homomorphisms between $\mathbb{Z} \star \mathbb{Z} $ and $\mathbb{Z} _2 $

Published on 09 Apr 2026 - 23:30

score 282 · Answer 8 · 2026-04-14 09:41:42

282

Views

Free groups as free product of infinite cyclic groups

Published on 14 Apr 2026 - 9:41

score 243 · Answer 9 · 2026-03-26 02:54:06

243

Views

Subgroup of $\mathbb{Z}\ast \mathbb{Z}$

Published on 26 Mar 2026 - 2:54

score 124 · Answer 10 · 2026-04-15 21:52:27

124

Views

Presentation of the amalgamated product of $G_1$ and $G_2$ above $H$ is $ \langle S_1,S_2\; ; \; R_1,R_2,\phi_1(s)\phi_{2}^{-1}(s),s \in S \rangle $

Published on 15 Apr 2026 - 21:52

score 82 · Answer 11 · 2026-05-10 17:39:02

82

Views

Are the central quotients of braid groups non-trivial free products?

Published on 10 May 2026 - 17:39

score 109 · Answer 12 · 2026-04-14 06:44:32

109

Views

Characterization of free product of groups by lifting property with respect to morphisms with right inverse

Published on 14 Apr 2026 - 6:44

score 98 · Answer 13 · 2026-04-11 17:57:41

98

Views

Free Products - representation of 1 by empty word is unique

Published on 11 Apr 2026 - 17:57

score 149 · Answer 14 · 2026-04-13 23:36:25

149

Views

Relation between finite residuals and free products.

Published on 13 Apr 2026 - 23:36

score 126 · Answer 15 · 2026-04-11 01:39:26

126

Views

Good introduction to free groups and free products

Published on 11 Apr 2026 - 1:39

List Question

Intuition of characteristic property of the free group

Understanding the free product amalgamation with an example

$\mathbb{Z}\ast\mathbb{Z}\ast\mathbb{Z}$ is an index two subgroup of $\mathbb{Z}\ast\mathbb{Z}$

Quotient of amalgamated free product by normal subgroup

Showing that the free group of a disjoint union is isomorphic to the free product of the corresponding free groups

Why does no non-trivial reduced words in $H_1 \backslash \{e\} \sqcup H_2 \backslash \{e\}$ imply that $\left< H_1, H_2 \right> = H_1 \ast H_2$?

Homomorphisms between $\mathbb{Z} \star \mathbb{Z} $ and $\mathbb{Z} _2 $

Free groups as free product of infinite cyclic groups

Subgroup of $\mathbb{Z}\ast \mathbb{Z}$

Presentation of the amalgamated product of $G_1$ and $G_2$ above $H$ is $ \langle S_1,S_2\; ; \; R_1,R_2,\phi_1(s)\phi_{2}^{-1}(s),s \in S \rangle $

Are the central quotients of braid groups non-trivial free products?

Characterization of free product of groups by lifting property with respect to morphisms with right inverse

Free Products - representation of 1 by empty word is unique

Relation between finite residuals and free products.

Good introduction to free groups and free products

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