Question

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

score 20.6k · Answer 1 · 2026-03-25 19:02:21

20.6k

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

Published on 25 Mar 2026 - 19:02

score 339 · Answer 2 · 2014-12-23 15:50:07

339

Views

Show that the group is cyclic.

Published on 23 Dec 2014 - 15:50

score 74 · Answer 3 · 2014-12-30 14:48:06

74

Views

$(\mathbb Z/6\mathbb Z)/(2\mathbb Z/6\mathbb Z)$

Published on 30 Dec 2014 - 14:48

score 204 · Answer 4 · 2015-01-01 16:35:12

204

Views

$O(G)=p^2 $, $p$ prime, $|Z(G)|>1$; prove $G$ abelian

Published on 01 Jan 2015 - 16:35

score 89 · Answer 5 · 2019-10-03 21:04:01

89

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Verify each of the following equalities for subgroups of $\mathbb Z$: $\langle24, -36, 54\rangle=\langle6\rangle$

Published on 03 Oct 2019 - 21:04

score 268 · Answer 6 · 2026-03-29 04:48:20

268

Views

normalizer of a cyclic group

Published on 29 Mar 2026 - 4:48

score 46 · Answer 7 · 2019-10-08 21:30:19

46

Views

Simplify the following expression in $\Bbb Z_4\times S_4$: $([2],(123))^{-1}([1],(24))([2],(123)).$

Published on 08 Oct 2019 - 21:30

score 94 · Answer 8 · 2019-10-08 22:59:33

94

Views

Find necessary and sufficient conditions on a subset $S$ of a group $G$ for $S=\langle S\rangle.$

Published on 08 Oct 2019 - 22:59

score 38 · Answer 9 · 2019-10-09 07:40:38

38

Views

Question on proof on Euler Toient function property.

Published on 09 Oct 2019 - 7:40

score 100 · Answer 10 · 2026-03-27 18:35:43

100

Views

Are there some commutative function to produce (pseudo) random numbers?

Published on 27 Mar 2026 - 18:35

score 1.1k · Answer 11 · 2019-10-10 00:59:37

1.1k

Views

Cyclic proper subgroups of a Non-Cyclic Group

Published on 10 Oct 2019 - 0:59

score 385 · Answer 12 · 2026-03-26 19:38:03

385

Views

Finding a generator for the intersection of two subgroups

Published on 26 Mar 2026 - 19:38

score 6.7k · Answer 13 · 2019-10-11 21:46:27

6.7k

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Systematically list the cyclic subgroups of $U(30)$.

Published on 11 Oct 2019 - 21:46

score 175 · Answer 14 · 2019-10-11 23:30:16

175

Views

Understanding Subgroups of $Z_n$ Specifically, $Z_8$

Published on 11 Oct 2019 - 23:30

score 34 · Answer 15 · 2019-10-13 00:53:22

34

Views

Free torsion part of centralizer of a cyclic group

Published on 13 Oct 2019 - 0:53

List Question

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

Show that the group is cyclic.

$(\mathbb Z/6\mathbb Z)/(2\mathbb Z/6\mathbb Z)$

$O(G)=p^2 $, $p$ prime, $|Z(G)|>1$; prove $G$ abelian

Verify each of the following equalities for subgroups of $\mathbb Z$: $\langle24, -36, 54\rangle=\langle6\rangle$

normalizer of a cyclic group

Simplify the following expression in $\Bbb Z_4\times S_4$: $([2],(123))^{-1}([1],(24))([2],(123)).$

Find necessary and sufficient conditions on a subset $S$ of a group $G$ for $S=\langle S\rangle.$

Question on proof on Euler Toient function property.

Are there some commutative function to produce (pseudo) random numbers?

Cyclic proper subgroups of a Non-Cyclic Group

Finding a generator for the intersection of two subgroups

Systematically list the cyclic subgroups of $U(30)$.

Understanding Subgroups of $Z_n$ Specifically, $Z_8$

Free torsion part of centralizer of a cyclic group

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