Question

An Infinite Cyclic Group has Exactly Two Generators: Is My Proof Correct?

score 20.6k · Answer 1 · 2014-12-20 20:04:52

20.6k

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An Infinite Cyclic Group has Exactly Two Generators: Is My Proof Correct?

Published on 20 Dec 2014 - 20:04

score 95 · Answer 2 · 2014-12-23 21:36:35

95

Views

Purely algebraic proof of stable commutator length in a finitely generated solvable group

Published on 23 Dec 2014 - 21:36

score 809 · Answer 3 · 2014-12-24 03:20:55

809

Views

Weird isomorphisms of infinite groups

Published on 24 Dec 2014 - 3:20

score 57 · Answer 4 · 2014-12-28 09:39:07

For any integers $m,n,r>1$ , does there exist an infinite group $G$,with elements $a,b\in G$ such that $o(a)=m , o(b)=n , o(ab)=r $?

score 167 · Answer 5 · 2014-12-28 09:57:16

For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?

score 149 · Answer 6 · 2019-10-05 12:05:35

149

Views

Random walk on infinite group - Entropy Speed and Growth

Published on 05 Oct 2019 - 12:05

score 44 · Answer 7 · 2019-10-06 00:10:17

44

Views

Do the finite groups of Lie type have infinite analogs?

Published on 06 Oct 2019 - 0:10

score 32 · Answer 8 · 2026-03-25 09:22:36

32

Views

Can all nonlinear groups be represented by integral transforms?

Published on 25 Mar 2026 - 9:22

score 236 · Answer 9 · 2019-10-09 20:32:54

236

Views

Isomorphic subgroups such that the quotient is isomorphic.

Published on 09 Oct 2019 - 20:32

score 141 · Answer 10 · 2026-03-24 22:42:14

141

Views

Question about a group-theoretic Chinese remainder theorem and intersections of normal finite-index subgroups

Published on 24 Mar 2026 - 22:42

score 119 · Answer 11 · 2026-02-23 06:38:00

119

Views

Showing that finding all subgroups of an (infinite) group is undecidable.

Published on 23 Feb 2026 - 6:38

score 1.6k · Answer 12 · 2019-10-18 21:04:08

1.6k

Views

Every infinite group has a non-trivial subgroup

Published on 18 Oct 2019 - 21:04

score 91 · Answer 13 · 2019-11-03 19:34:24

91

Views

Let $H =\mathbb{Z}/2\mathbb{Z}\times G$ I want to show that H is isomorphic to a subgroup of $G$ and vice-versa

Published on 03 Nov 2019 - 19:34

score 320 · Answer 14 · 2026-03-25 14:24:45

320

Views

Fitting subgroups of infinite groups

Published on 25 Mar 2026 - 14:24

score 90 · Answer 15 · 2019-11-08 20:19:40

90

Views

Locally cyclic quotient and locally cyclic subgroup

Published on 08 Nov 2019 - 20:19

List Question

An Infinite Cyclic Group has Exactly Two Generators: Is My Proof Correct?

Purely algebraic proof of stable commutator length in a finitely generated solvable group

Weird isomorphisms of infinite groups

For any integers $m,n,r>1$ , does there exist an infinite group $G$,with elements $a,b\in G$ such that $o(a)=m , o(b)=n , o(ab)=r $?

For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?

Random walk on infinite group - Entropy Speed and Growth

Do the finite groups of Lie type have infinite analogs?

Can all nonlinear groups be represented by integral transforms?

Isomorphic subgroups such that the quotient is isomorphic.

Question about a group-theoretic Chinese remainder theorem and intersections of normal finite-index subgroups

Showing that finding all subgroups of an (infinite) group is undecidable.

Every infinite group has a non-trivial subgroup

Let $H =\mathbb{Z}/2\mathbb{Z}\times G$ I want to show that H is isomorphic to a subgroup of $G$ and vice-versa

Fitting subgroups of infinite groups

Locally cyclic quotient and locally cyclic subgroup

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