Question

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

score 20.6k · Answer 1 · 2026-04-13 00:15:13

20.6k

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

Published on 13 Apr 2026 - 0:15

score 98 · Answer 2 · 2026-04-11 02:36:59

98

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

Published on 11 Apr 2026 - 2:36

score 812 · Answer 3 · 2026-04-10 18:51:07

812

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Weird isomorphisms of infinite groups

Published on 10 Apr 2026 - 18:51

score 60 · Answer 4 · 2026-04-17 04:47:09

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 170 · Answer 5 · 2026-04-16 15:12:51

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 150 · Answer 6 · 2026-03-25 22:03:24

150

Views

Random walk on infinite group - Entropy Speed and Growth

Published on 25 Mar 2026 - 22:03

score 45 · Answer 7 · 2026-03-25 19:05:44

45

Views

Do the finite groups of Lie type have infinite analogs?

Published on 25 Mar 2026 - 19:05

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 237 · Answer 9 · 2026-03-25 19:02:22

237

Views

Isomorphic subgroups such that the quotient is isomorphic.

Published on 25 Mar 2026 - 19:02

score 158 · Answer 10 · 2026-05-01 17:33:35

158

Views

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

Published on 01 May 2026 - 17:33

score 120 · Answer 11 · 2026-04-09 10:06:31

120

Views

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

Published on 09 Apr 2026 - 10:06

score 1.6k · Answer 12 · 2026-03-25 19:03:05

1.6k

Views

Every infinite group has a non-trivial subgroup

Published on 25 Mar 2026 - 19:03

score 94 · Answer 13 · 2026-04-16 20:34:37

94

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 16 Apr 2026 - 20:34

score 321 · Answer 14 · 2026-05-10 17:58:24

321

Views

Fitting subgroups of infinite groups

Published on 10 May 2026 - 17:58

score 91 · Answer 15 · 2026-03-25 19:03:12

91

Views

Locally cyclic quotient and locally cyclic subgroup

Published on 25 Mar 2026 - 19:03

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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