Question

All possible non-isomorphic abelian groups of order $225$ and the minimum possible collapsion

score 490 · Answer 1 · 2026-04-25 21:54:35

490

Views

All possible non-isomorphic abelian groups of order $225$ and the minimum possible collapsion

Published on 25 Apr 2026 - 21:54

score 202 · Answer 2 · 2026-04-25 21:54:35

202

Views

Torsion subgroup combined with normal subgroup!

Published on 25 Apr 2026 - 21:54

score 69 · Answer 3 · 2026-04-29 12:52:52

69

Views

Uniqueness of total orders on abelian groups

Published on 29 Apr 2026 - 12:52

score 1.1k · Answer 4 · 2026-05-07 08:47:29

1.1k

Views

Center of Simple Abelian Group and Simple Nonabelian Group

Published on 07 May 2026 - 8:47

score 489 · Answer 5 · 2026-04-25 21:57:46

489

Views

Two abelian groups are isomorphic iff their corresponding sylow subgroups are isomorphic.

Published on 25 Apr 2026 - 21:57

score 83 · Answer 6 · 2026-05-02 23:46:21

83

Views

How can I express a resulting discrepancy? (Proving $\varphi(x \in G) = x^{-1}$ is an automorphism iff G is abelian)

Published on 02 May 2026 - 23:46

score 176 · Answer 7 · 2026-04-25 21:54:35

176

Views

How order of an element and gcd related for abelian groups

Published on 25 Apr 2026 - 21:54

score 290 · Answer 8 · 2026-05-05 10:19:33

290

Views

$\mathrm{Hom}(\mathrm{Hom}(G,H),H) \simeq G$?

Published on 05 May 2026 - 10:19

score 746 · Answer 9 · 2026-04-29 12:44:22

746

Views

Abelian Groups and Homomorphic Images of Free Abelian Groups

Published on 29 Apr 2026 - 12:44

score 43 · Answer 10 · 2026-05-03 23:52:05

43

Views

Abelian group - set $G$ of all complex roots of $1$, of all possible orders

Published on 03 May 2026 - 23:52

score 330 · Answer 11 · 2026-04-29 12:24:33

330

Views

Isomorphism about direct product of multiplicative group and direct product of additive group

Published on 29 Apr 2026 - 12:24

score 1k · Answer 12 · 2026-04-25 21:54:36

1k

Views

Proof verification: Prove whether or not every proper subgroup of a nonabelian group is nonabelian.

Published on 25 Apr 2026 - 21:54

score 150 · Answer 13 · 2026-04-25 21:53:11

150

Views

Let $H\leq G$. If $g\in G$, show that $gHg^{-1}=\left \{ g^{-1}hg:h\in H,g\in G \right \}$ is a subgroup of $G$.

Published on 25 Apr 2026 - 21:53

score 1.4k · Answer 14 · 2026-04-25 21:53:59

1.4k

Views

Proof verification: If $xy=x^{-1}y^{-1}$ for all $x,y\in G$, then $G$ is abelian.

Published on 25 Apr 2026 - 21:53

score 322 · Answer 15 · 2026-04-29 12:42:46

322

Views

Cannot follow proof that refinement of solvable series is also solvable

Published on 29 Apr 2026 - 12:42

List Question

All possible non-isomorphic abelian groups of order $225$ and the minimum possible collapsion

Torsion subgroup combined with normal subgroup!

Uniqueness of total orders on abelian groups

Center of Simple Abelian Group and Simple Nonabelian Group

Two abelian groups are isomorphic iff their corresponding sylow subgroups are isomorphic.

How can I express a resulting discrepancy? (Proving $\varphi(x \in G) = x^{-1}$ is an automorphism iff G is abelian)

How order of an element and gcd related for abelian groups

$\mathrm{Hom}(\mathrm{Hom}(G,H),H) \simeq G$?

Abelian Groups and Homomorphic Images of Free Abelian Groups

Abelian group - set $G$ of all complex roots of $1$, of all possible orders

Isomorphism about direct product of multiplicative group and direct product of additive group

Proof verification: Prove whether or not every proper subgroup of a nonabelian group is nonabelian.

Let $H\leq G$. If $g\in G$, show that $gHg^{-1}=\left \{ g^{-1}hg:h\in H,g\in G \right \}$ is a subgroup of $G$.

Proof verification: If $xy=x^{-1}y^{-1}$ for all $x,y\in G$, then $G$ is abelian.

Cannot follow proof that refinement of solvable series is also solvable

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