List questions from cyclic-groups

Published on 09 Apr 2015 - 13:53

70

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133

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Is $\mathbb{Z}\times\mathbb{Z}/\langle(6,5),(3,4)\rangle$ finitely generated?

Published on 14 Apr 2015 - 22:10

113

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Subgroup of a cyclic finite group

Published on 15 Apr 2015 - 18:49

519

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Quotient group(Factor group)

Published on 26 Mar 2026 - 22:11

218

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Looking for different proofs for $-1$ is a quadratic residue of primes of the form $4k+1$ and related facts

Published on 28 Mar 2026 - 3:55

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Why is the set of integers with the operation of addition considered a cyclic group?

Published on 19 Apr 2015 - 18:17

162

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Group theory disjoint cycles

Published on 23 Apr 2015 - 7:20

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Help to prove that $ U_{p} $ is a cyclic group.

Published on 29 Mar 2026 - 4:09

140

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Is a finite cyclic group a Poincare duality group?

Published on 25 Mar 2026 - 19:11

48

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Clarification for question: Homomorphisms from $\Bbb Z / n \to \Bbb C_{\ne 0}$

Published on 30 Apr 2015 - 6:08

318

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What are all the subgroups of $\Bbb{Z}/10\Bbb{Z}$?

Published on 03 May 2015 - 14:10

99

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Is the direct product $\Bbb Z \times \Bbb Z$ with operation $(n,m)+(p,q):=(n+p,m+q)$ a cyclic group?

Published on 04 May 2015 - 22:40

465

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$|G|=p_1p_2p_3$ distinct primes with $p_i \nmid p_j-1$ then $G$ is cyclic

Published on 30 Mar 2026 - 2:07

49

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Groups and Subgroups elements

Published on 07 May 2015 - 3:32

List Question

Can a cyclic group have more than two generators?

Question about exponents of groups

Is $\mathbb{Z}\times\mathbb{Z}/\langle(6,5),(3,4)\rangle$ finitely generated?

Subgroup of a cyclic finite group

Quotient group(Factor group)

Looking for different proofs for $-1$ is a quadratic residue of primes of the form $4k+1$ and related facts

Why is the set of integers with the operation of addition considered a cyclic group?

Group theory disjoint cycles

Help to prove that $ U_{p} $ is a cyclic group.

Is a finite cyclic group a Poincare duality group?

Clarification for question: Homomorphisms from $\Bbb Z / n \to \Bbb C_{\ne 0}$

What are all the subgroups of $\Bbb{Z}/10\Bbb{Z}$?

Is the direct product $\Bbb Z \times \Bbb Z$ with operation $(n,m)+(p,q):=(n+p,m+q)$ a cyclic group?

$|G|=p_1p_2p_3$ distinct primes with $p_i \nmid p_j-1$ then $G$ is cyclic

Groups and Subgroups elements

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