Question

If the order of $\langle a\rangle$ is finite, then the distinct elements of $G$ are $e,a,a^2,a^3,...,a^{n-1}$

score 48 · Answer 1 · 2020-12-16 08:39:42

48

Views

If the order of $\langle a\rangle$ is finite, then the distinct elements of $G$ are $e,a,a^2,a^3,...,a^{n-1}$

Published on 16 Dec 2020 - 8:39

score 66 · Answer 2 · 2026-03-30 09:44:00

66

Views

Split short exact sequence contradiction

Published on 30 Mar 2026 - 9:44

score 83 · Answer 3 · 2020-12-19 14:58:39

83

Views

Equidistant points by modular arithmetic

Published on 19 Dec 2020 - 14:58

score 854 · Answer 4 · 2020-12-21 18:54:27

854

Views

If G is finite cyclic group then why is it true that for every divisor of the cardinality of $G$, there only exists at most one subgroup?

Published on 21 Dec 2020 - 18:54

score 137 · Answer 5 · 2020-12-22 17:15:23

137

Views

number of elements of order $d$ in a cyclic group

Published on 22 Dec 2020 - 17:15

score 244 · Answer 6 · 2020-12-23 07:36:15

244

Views

How is it possible that a cyclic group like $\mathbb Z_{2p}$ is isomorphic to a non-cyclic group of order $2p$?

Published on 23 Dec 2020 - 7:36

score 42 · Answer 7 · 2020-12-30 14:28:30

42

Views

$\sigma^p$ is the product of p cycles of length q

Published on 30 Dec 2020 - 14:28

score 523 · Answer 8 · 2026-03-31 18:42:31

523

Views

If $p$ is an odd prime then prove that there cannot exist a finite group $G$ such that ${\rm Aut}(G)\cong \mathbb{Z}_p$.

Published on 31 Mar 2026 - 18:42

score 246 · Answer 9 · 2021-01-01 20:33:53

246

Views

Existence of a $\mathbb{Z} _{15}$ in a group $G$ where $|G|=3 \cdot 5 \cdot 17$

Published on 01 Jan 2021 - 20:33

score 92 · Answer 10 · 2026-03-28 10:29:20

92

Views

$G$ is cyclic of order $10$, describe all quotients of $G$

Published on 28 Mar 2026 - 10:29

score 177 · Answer 11 · 2026-04-03 15:41:22

177

Views

Finding the kernel of homomorphism between two cyclic groups

Published on 03 Apr 2026 - 15:41

score 74 · Answer 12 · 2021-01-07 22:57:36

74

Views

Why is $\Bbb Z_3$ cyclic?

Published on 07 Jan 2021 - 22:57

score 74 · Answer 13 · 2021-01-08 20:01:11

74

Views

Set which can't be transformed into a cyclic group

Published on 08 Jan 2021 - 20:01

score 94 · Answer 14 · 2026-03-26 04:52:27

94

Views

Almost nilpotent groups of hyperbolic isometries are cyclic

Published on 26 Mar 2026 - 4:52

score 581 · Answer 15 · 2026-03-28 10:29:20

581

Views

Prove or disprove: If $H$ is a normal subgroup and cyclic and $G/H$ are cyclic, then $G$ is cyclic.

Published on 28 Mar 2026 - 10:29

List Question

If the order of $\langle a\rangle$ is finite, then the distinct elements of $G$ are $e,a,a^2,a^3,...,a^{n-1}$

Split short exact sequence contradiction

Equidistant points by modular arithmetic

If G is finite cyclic group then why is it true that for every divisor of the cardinality of $G$, there only exists at most one subgroup?

number of elements of order $d$ in a cyclic group

How is it possible that a cyclic group like $\mathbb Z_{2p}$ is isomorphic to a non-cyclic group of order $2p$?

$\sigma^p$ is the product of p cycles of length q

If $p$ is an odd prime then prove that there cannot exist a finite group $G$ such that ${\rm Aut}(G)\cong \mathbb{Z}_p$.

Existence of a $\mathbb{Z} _{15}$ in a group $G$ where $|G|=3 \cdot 5 \cdot 17$

$G$ is cyclic of order $10$, describe all quotients of $G$

Finding the kernel of homomorphism between two cyclic groups

Why is $\Bbb Z_3$ cyclic?

Set which can't be transformed into a cyclic group

Almost nilpotent groups of hyperbolic isometries are cyclic

Prove or disprove: If $H$ is a normal subgroup and cyclic and $G/H$ are cyclic, then $G$ is cyclic.

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