Question

The group of non zero real or imaginary numbers

score 123 · Answer 1 · 2020-05-24 10:32:59

123

Views

The group of non zero real or imaginary numbers

Published on 24 May 2020 - 10:32

score 50 · Answer 2 · 2026-03-28 06:10:19

50

Views

Let $G$ be a non-nilpotent group where all the non-normal abelian subgroups of $G$ are cyclic. Then $G$ has cyclic center.

Published on 28 Mar 2026 - 6:10

score 41 · Answer 3 · 2026-03-26 16:07:06

41

Views

G is a commutative group of order 2*N, how to prove G has a N-order quotient group?

Published on 26 Mar 2026 - 16:07

score 135 · Answer 4 · 2020-05-26 13:57:35

135

Views

If $G$ is an Abelian Group of rank $r$ then $G\otimes_\mathbb{Z}\mathbb{Q}$ is isomorphic to $\mathbb{Q}^r$

Published on 26 May 2020 - 13:57

score 103 · Answer 5 · 2020-05-27 17:58:02

103

Views

Let G be a Group and $a,b \in G$. If $a$ and $b$ commute and $|a|$ and $|b|$ are finite. What can be possible values for $|ab|$?

Published on 27 May 2020 - 17:58

score 31 · Answer 6 · 2020-05-28 16:23:48

31

Views

Is there a name for this kind of subgroup?

Published on 28 May 2020 - 16:23

score 801 · Answer 7 · 2026-03-30 07:42:42

801

Views

If $G$ is an Abelian group and contains cyclic subgroups of order 4 and 6, what other sizes of cyclic group G must contain?

Published on 30 Mar 2026 - 7:42

score 262 · Answer 8 · 2020-06-01 16:02:13

262

Views

How to construct additive inverse in an abelian category

Published on 01 Jun 2020 - 16:02

score 294 · Answer 9 · 2026-03-26 09:45:53

294

Views

What does the abelianization mean?

Published on 26 Mar 2026 - 9:45

score 76 · Answer 10 · 2020-06-02 16:21:59

76

Views

How to show that $H=\langle a,b\rangle=\{a^m\cdot{b^n}\mid m,n\in{\mathbb{Z}}\}$ is a subgroup of $\langle G,\cdot\rangle$?

Published on 02 Jun 2020 - 16:21

score 474 · Answer 11 · 2026-03-26 04:52:11

474

Views

Grothendieck group "commutes" with direct sum

Published on 26 Mar 2026 - 4:52

score 200 · Answer 12 · 2026-03-28 07:51:51

200

Views

Product $PN$ of normal subgroups is abelian

Published on 28 Mar 2026 - 7:51

score 149 · Answer 13 · 2026-03-28 08:31:03

149

Views

Isomorphism between $SO_2\tilde{\times}\mathbb{Z}_2$ and $O_2$

Published on 28 Mar 2026 - 8:31

score 253 · Answer 14 · 2026-03-26 09:37:21

253

Views

Torsion Points over complex Elliptic Curves

Published on 26 Mar 2026 - 9:37

score 60 · Answer 15 · 2020-06-05 19:16:34

60

Views

Basis of finitely generated abelian group with bounded norms (exercise from Lang's Algebra)

Published on 05 Jun 2020 - 19:16

List Question

The group of non zero real or imaginary numbers

Let $G$ be a non-nilpotent group where all the non-normal abelian subgroups of $G$ are cyclic. Then $G$ has cyclic center.

G is a commutative group of order 2*N, how to prove G has a N-order quotient group?

If $G$ is an Abelian Group of rank $r$ then $G\otimes_\mathbb{Z}\mathbb{Q}$ is isomorphic to $\mathbb{Q}^r$

Let G be a Group and $a,b \in G$. If $a$ and $b$ commute and $|a|$ and $|b|$ are finite. What can be possible values for $|ab|$?

Is there a name for this kind of subgroup?

If $G$ is an Abelian group and contains cyclic subgroups of order 4 and 6, what other sizes of cyclic group G must contain?

How to construct additive inverse in an abelian category

What does the abelianization mean?

How to show that $H=\langle a,b\rangle=\{a^m\cdot{b^n}\mid m,n\in{\mathbb{Z}}\}$ is a subgroup of $\langle G,\cdot\rangle$?

Grothendieck group "commutes" with direct sum

Product $PN$ of normal subgroups is abelian

Isomorphism between $SO_2\tilde{\times}\mathbb{Z}_2$ and $O_2$

Torsion Points over complex Elliptic Curves

Basis of finitely generated abelian group with bounded norms (exercise from Lang's Algebra)

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