Question

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

score 829 · Answer 1 · 2026-05-04 04:02:20

829

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

Published on 04 May 2026 - 4:02

score 79 · Answer 2 · 2026-05-03 04:37:23

79

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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 03 May 2026 - 4:37

score 6.2k · Answer 3 · 2026-05-05 04:14:39

6.2k

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

Published on 05 May 2026 - 4:14

score 95 · Answer 4 · 2026-05-05 04:12:12

95

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

Published on 05 May 2026 - 4:12

score 241 · Answer 5 · 2026-05-07 04:05:08

241

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Bases of Subgroups of Infinitely Generated Free Abelian Groups

Published on 07 May 2026 - 4:05

score 219 · Answer 6 · 2026-04-21 10:58:26

219

Views

Question on the definition of Free Abelian Groups

Published on 21 Apr 2026 - 10:58

score 40 · Answer 7 · 2026-04-29 12:44:21

40

Views

Taking a basis from an old basis in Free Abelian Groups

Published on 29 Apr 2026 - 12:44

score 288 · Answer 8 · 2026-05-05 04:12:18

288

Views

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

Published on 05 May 2026 - 4:12

score 86 · Answer 9 · 2026-04-29 12:44:21

86

Views

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

Published on 29 Apr 2026 - 12:44

score 54 · Answer 10 · 2026-05-06 20:32:14

54

Views

Conditions under which a union of free abelian groups is free

Published on 06 May 2026 - 20:32

score 64 · Answer 11 · 2026-04-29 12:44:28

64

Views

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

Published on 29 Apr 2026 - 12:44

score 451 · Answer 12 · 2026-04-28 20:03:55

451

Views

Amount of elements of order $p^2$

Published on 28 Apr 2026 - 20:03

score 185 · Answer 13 · 2026-04-22 18:54:12

185

Views

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

Published on 22 Apr 2026 - 18:54

score 246 · Answer 14 · 2026-04-29 12:44:23

246

Views

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

Published on 29 Apr 2026 - 12:44

score 115 · Answer 15 · 2026-04-29 12:44:22

115

Views

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

Published on 29 Apr 2026 - 12:44

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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