Question

$\mathbb Z \oplus \mathbb Z \oplus \mathbb Q \equiv \mathbb Z \oplus \mathbb Q \oplus \mathbb Q$?

score 92 · Answer 1 · 2020-05-11 20:42:38

92

Views

$\mathbb Z \oplus \mathbb Z \oplus \mathbb Q \equiv \mathbb Z \oplus \mathbb Q \oplus \mathbb Q$?

Published on 11 May 2020 - 20:42

score 469 · Answer 2 · 2020-05-14 14:44:40

469

Views

Proof that a finite abelian group has a subgroup of order $n$ for every $n$ which divides $|G|$

Published on 14 May 2020 - 14:44

score 190 · Answer 3 · 2026-03-29 15:15:18

190

Views

Number of group homomorphism from $ \mathbb{Z}_{2} * \mathbb{Z}_{2} \to D_{8}$.

Published on 29 Mar 2026 - 15:15

score 46 · Answer 4 · 2026-03-26 02:54:04

46

Views

The longest cycle and relation between the generating elements of a Cayley graph

Published on 26 Mar 2026 - 2:54

score 62 · Answer 5 · 2020-05-15 19:15:14

62

Views

Let $f:G \to H$ where $|G|=pq$ where $p,q$ primes, then $H \cong G$ or $H$ abelian.

Published on 15 May 2020 - 19:15

score 140 · Answer 6 · 2020-05-16 11:22:43

140

Views

Group of order $pq, p \leq q, p \not\mid q - 1$ is abelian

Published on 16 May 2020 - 11:22

score 319 · Answer 7 · 2026-03-30 07:08:57

319

Views

On the proof of classification of finitely generated abelian groups

Published on 30 Mar 2026 - 7:08

score 87 · Answer 8 · 2026-03-29 03:35:49

87

Views

What's the form of the subgroups of $(\mathbb{Q}_p/\mathbb{Z}_p)^2$?

Published on 29 Mar 2026 - 3:35

score 278 · Answer 9 · 2026-03-28 06:13:22

278

Views

Clarification on proof of fundamental theorem of finite abelian groups

Published on 28 Mar 2026 - 6:13

score 245 · Answer 10 · 2026-03-25 23:10:07

245

Views

Finding the group order from the presentation of a group and deciding if it is abelian

Published on 25 Mar 2026 - 23:10

score 322 · Answer 11 · 2026-03-27 11:47:52

322

Views

Short exact sequences of finite abelian groups

Published on 27 Mar 2026 - 11:47

score 498 · Answer 12 · 2026-03-25 11:11:57

498

Views

A $p$-group of exponent $p$

Published on 25 Mar 2026 - 11:11

score 1.4k · Answer 13 · 2026-03-25 20:33:30

1.4k

Views

If $N$ is a normal subgroup of $G$, and $N \cap [G,G]=\{e\}$, then $N$ is contained in $Z(G)$.

Published on 25 Mar 2026 - 20:33

score 108 · Answer 14 · 2026-03-27 02:35:48

108

Views

Homology with Coefficients of an abelian group

Published on 27 Mar 2026 - 2:35

score 193 · Answer 15 · 2026-03-28 13:02:20

193

Views

Show $G\cong \ker(f) \times \mathbb{Z}$ for abelian $G$

Published on 28 Mar 2026 - 13:02

List Question

$\mathbb Z \oplus \mathbb Z \oplus \mathbb Q \equiv \mathbb Z \oplus \mathbb Q \oplus \mathbb Q$?

Proof that a finite abelian group has a subgroup of order $n$ for every $n$ which divides $|G|$

Number of group homomorphism from $ \mathbb{Z}_{2} * \mathbb{Z}_{2} \to D_{8}$.

The longest cycle and relation between the generating elements of a Cayley graph

Let $f:G \to H$ where $|G|=pq$ where $p,q$ primes, then $H \cong G$ or $H$ abelian.

Group of order $pq, p \leq q, p \not\mid q - 1$ is abelian

On the proof of classification of finitely generated abelian groups

What's the form of the subgroups of $(\mathbb{Q}_p/\mathbb{Z}_p)^2$?

Clarification on proof of fundamental theorem of finite abelian groups

Finding the group order from the presentation of a group and deciding if it is abelian

Short exact sequences of finite abelian groups

A $p$-group of exponent $p$

If $N$ is a normal subgroup of $G$, and $N \cap [G,G]=\{e\}$, then $N$ is contained in $Z(G)$.

Homology with Coefficients of an abelian group

Show $G\cong \ker(f) \times \mathbb{Z}$ for abelian $G$

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