Question

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

score 485 · Answer 1 · 2018-01-21 11:55:02

485

Views

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

Published on 21 Jan 2018 - 11:55

score 195 · Answer 2 · 2026-03-17 07:26:40

195

Views

Torsion subgroup combined with normal subgroup!

Published on 17 Mar 2026 - 7:26

score 64 · Answer 3 · 2026-03-17 07:40:49

64

Views

Uniqueness of total orders on abelian groups

Published on 17 Mar 2026 - 7:40

score 1k · Answer 4 · 2026-03-19 17:44:48

1k

Views

Center of Simple Abelian Group and Simple Nonabelian Group

Published on 19 Mar 2026 - 17:44

score 481 · Answer 5 · 2018-01-22 18:37:43

481

Views

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

Published on 22 Jan 2018 - 18:37

score 73 · Answer 6 · 2026-03-19 23:07:28

73

Views

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

Published on 19 Mar 2026 - 23:07

score 170 · Answer 7 · 2026-03-17 19:10:43

170

Views

How order of an element and gcd related for abelian groups

Published on 17 Mar 2026 - 19:10

score 285 · Answer 8 · 2026-03-19 22:03:31

285

Views

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

Published on 19 Mar 2026 - 22:03

score 738 · Answer 9 · 2026-03-20 04:15:59

738

Views

Abelian Groups and Homomorphic Images of Free Abelian Groups

Published on 20 Mar 2026 - 4:15

score 37 · Answer 10 · 2018-01-28 18:00:40

37

Views

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

Published on 28 Jan 2018 - 18:00

score 321 · Answer 11 · 2026-03-23 15:38:33

321

Views

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

Published on 23 Mar 2026 - 15:38

score 1k · Answer 12 · 2018-01-29 02:35:58

1k

Views

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

Published on 29 Jan 2018 - 2:35

score 145 · Answer 13 · 2018-01-29 04:12:50

145

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 29 Jan 2018 - 4:12

score 1.4k · Answer 14 · 2018-01-29 04:25:46

1.4k

Views

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

Published on 29 Jan 2018 - 4:25

score 315 · Answer 15 · 2026-03-20 09:39:26

315

Views

Cannot follow proof that refinement of solvable series is also solvable

Published on 20 Mar 2026 - 9:39

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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