Question

Help resolving this contradiction in descriptions of the fundamental groups of the figure eight and n-torus

score 821 · Answer 1 · 2026-03-20 07:55:44

821

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Help resolving this contradiction in descriptions of the fundamental groups of the figure eight and n-torus

Published on 20 Mar 2026 - 7:55

score 72 · Answer 2 · 2026-03-20 13:30:54

72

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Is it true that $(\mathbb{Z}\bigoplus\mathbb{Z}\bigoplus\mathbb{Z})/(\mathbb{Z}\bigoplus\mathbb{Z})\cong\mathbb{Z}$

Published on 20 Mar 2026 - 13:30

score 6.2k · Answer 3 · 2026-03-22 22:16:03

6.2k

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What is the definition of a free abelian group generated by the set $X$?

Published on 22 Mar 2026 - 22:16

score 86 · Answer 4 · 2026-03-22 17:02:32

86

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Invariant factor decomposition of $\mathbb{Z}_6 \otimes_{\mathbb{Z}} \mathbb{Z}_9$

Published on 22 Mar 2026 - 17:02

score 236 · Answer 5 · 2026-03-23 03:25:20

236

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Bases of Subgroups of Infinitely Generated Free Abelian Groups

Published on 23 Mar 2026 - 3:25

score 213 · Answer 6 · 2026-03-23 00:03:21

213

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Question on the definition of Free Abelian Groups

Published on 23 Mar 2026 - 0:03

score 34 · Answer 7 · 2026-03-22 19:28:53

34

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Taking a basis from an old basis in Free Abelian Groups

Published on 22 Mar 2026 - 19:28

score 281 · Answer 8 · 2026-03-22 20:31:51

281

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Show that $G/2G \cong (\mathbb{Z}/2)^n$, where $G$ is an abelian group and $G \cong \mathbb{Z}^n$

Published on 22 Mar 2026 - 20:31

score 77 · Answer 9 · 2026-03-22 19:54:45

77

Views

Taking free abelian groups "commutes" with quotient by equivalence relation

Published on 22 Mar 2026 - 19:54

score 41 · Answer 10 · 2026-03-17 17:28:36

41

Views

Conditions under which a union of free abelian groups is free

Published on 17 Mar 2026 - 17:28

score 57 · Answer 11 · 2026-03-22 21:22:56

57

Views

On isomorphism of quotient groups of free abelian groups of finite rank

Published on 22 Mar 2026 - 21:22

score 441 · Answer 12 · 2026-03-25 14:22:03

441

Views

Amount of elements of order $p^2$

Published on 25 Mar 2026 - 14:22

score 181 · Answer 13 · 2026-03-25 12:53:51

181

Views

How many epimorphisms from $F_2$ to $\mathbb{Z}_5$?

Published on 25 Mar 2026 - 12:53

score 236 · Answer 14 · 2026-03-25 16:03:40

236

Views

Elementary divisors of a subgroup of $\mathbb{Z^2}$ of index $36$

Published on 25 Mar 2026 - 16:03

score 112 · Answer 15 · 2026-03-25 14:25:58

112

Views

What could be the elementary divisors of subgroup of $\mathbb{Z}^2$

Published on 25 Mar 2026 - 14:25

List Question

Help resolving this contradiction in descriptions of the fundamental groups of the figure eight and n-torus

Is it true that $(\mathbb{Z}\bigoplus\mathbb{Z}\bigoplus\mathbb{Z})/(\mathbb{Z}\bigoplus\mathbb{Z})\cong\mathbb{Z}$

What is the definition of a free abelian group generated by the set $X$?

Invariant factor decomposition of $\mathbb{Z}_6 \otimes_{\mathbb{Z}} \mathbb{Z}_9$

Bases of Subgroups of Infinitely Generated Free Abelian Groups

Question on the definition of Free Abelian Groups

Taking a basis from an old basis in Free Abelian Groups

Show that $G/2G \cong (\mathbb{Z}/2)^n$, where $G$ is an abelian group and $G \cong \mathbb{Z}^n$

Taking free abelian groups "commutes" with quotient by equivalence relation

Conditions under which a union of free abelian groups is free

On isomorphism of quotient groups of free abelian groups of finite rank

Amount of elements of order $p^2$

How many epimorphisms from $F_2$ to $\mathbb{Z}_5$?

Elementary divisors of a subgroup of $\mathbb{Z^2}$ of index $36$

What could be the elementary divisors of subgroup of $\mathbb{Z}^2$

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