Question

Can the infinite cyclic group be understood as the group of all rational numbers under addition?

score 693 · Answer 1 · 2026-04-12 20:12:48

693

Views

Can the infinite cyclic group be understood as the group of all rational numbers under addition?

Published on 12 Apr 2026 - 20:12

score 160 · Answer 2 · 2026-04-14 14:27:10

160

Views

Terminology of homocyclic groups

Published on 14 Apr 2026 - 14:27

score 67 · Answer 3 · 2026-04-13 10:02:02

67

Views

When can we extend homomorphism from cyclic group?

Published on 13 Apr 2026 - 10:02

score 80 · Answer 4 · 2026-04-12 04:43:30

80

Views

Is a cyclic group considered a more specialized form of a "plain-ole" group?

Published on 12 Apr 2026 - 4:43

score 83 · Answer 5 · 2026-04-15 21:29:10

83

Views

Why is it assuming in both sides that $a^{n}=e$?

Published on 15 Apr 2026 - 21:29

score 1.2k · Answer 6 · 2026-04-11 17:18:01

1.2k

Views

How to calculate the homology/cohomology of a finite cyclic group

Published on 11 Apr 2026 - 17:18

score 87 · Answer 7 · 2026-04-15 03:58:30

87

Views

Find a generator of the intersection of three subgroups of the integers

Published on 15 Apr 2026 - 3:58

score 1.3k · Answer 8 · 2026-04-12 21:24:24

1.3k

Views

Is every group (Z/nZ, +) isomorphic to some subgroup of $(Z/mZ)^\times$? If not, find all n for which this doesn't hold

Published on 12 Apr 2026 - 21:24

score 378 · Answer 9 · 2026-04-11 20:21:36

378

Views

Proof on relationship between generators and order of a cyclic group.

Published on 11 Apr 2026 - 20:21

score 658 · Answer 10 · 2026-04-11 23:11:54

658

Views

When is the unit group of a ring R cyclic?

Published on 11 Apr 2026 - 23:11

score 112 · Answer 11 · 2026-04-11 10:49:16

112

Views

Is it possible to have two different cyclic decompositions with same annihilators? how about in rational canonical form?

Published on 11 Apr 2026 - 10:49

score 51 · Answer 12 · 2026-04-14 04:26:16

51

Views

Abstract Algebra - Size of the generating set

Published on 14 Apr 2026 - 4:26

score 168 · Answer 13 · 2026-04-13 09:43:29

168

Views

Use Fundamental Theorem of Finite Abelian Groups to show that subgroup is cyclic

Published on 13 Apr 2026 - 9:43

score 1.4k · Answer 14 · 2026-04-15 11:42:20

1.4k

Views

Galois Group of $x^p-1$ cyclic

Published on 15 Apr 2026 - 11:42

score 583 · Answer 15 · 2026-05-10 13:24:47

583

Views

$M$ is a cyclic module if and only if it has a single invariant factor

Published on 10 May 2026 - 13:24

List Question

Can the infinite cyclic group be understood as the group of all rational numbers under addition?

Terminology of homocyclic groups

When can we extend homomorphism from cyclic group?

Is a cyclic group considered a more specialized form of a "plain-ole" group?

Why is it assuming in both sides that $a^{n}=e$?

How to calculate the homology/cohomology of a finite cyclic group

Find a generator of the intersection of three subgroups of the integers

Is every group (Z/nZ, +) isomorphic to some subgroup of $(Z/mZ)^\times$? If not, find all n for which this doesn't hold

Proof on relationship between generators and order of a cyclic group.

When is the unit group of a ring R cyclic?

Is it possible to have two different cyclic decompositions with same annihilators? how about in rational canonical form?

Abstract Algebra - Size of the generating set

Use Fundamental Theorem of Finite Abelian Groups to show that subgroup is cyclic

Galois Group of $x^p-1$ cyclic

$M$ is a cyclic module if and only if it has a single invariant factor

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