Question

Confusion about the last step of this proof of " Every subgroup of a cyclic group is cyclic":does not subcase $2.2$ contradict the desired conclusion

score 75 · Answer 1 · 2022-01-09 12:20:24

75

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Confusion about the last step of this proof of " Every subgroup of a cyclic group is cyclic":does not subcase $2.2$ contradict the desired conclusion

Published on 09 Jan 2022 - 12:20

score 467 · Answer 2 · 2022-01-09 17:04:48

467

Views

Let $G$ be a abelian group such that $|G| = 2p$ and $p$ Is a odd prime number. Prove $G$ is a cyclic group.

Published on 09 Jan 2022 - 17:04

score 100 · Answer 3 · 2022-01-10 21:22:34

100

Views

Does this contradict my definition of "cyclic"?

Published on 10 Jan 2022 - 21:22

score 293 · Answer 4 · 2026-03-29 07:19:50

293

Views

Question about "Quotient Group of Cyclic Group is Cyclic"

Published on 29 Mar 2026 - 7:19

score 73 · Answer 5 · 2022-01-17 00:07:07

73

Views

Asking for clarification in a group theory proof

Published on 17 Jan 2022 - 0:07

score 86 · Answer 6 · 2026-03-29 07:29:21

86

Views

Groups of order $16$ with a cyclic quotient of order $4$

Published on 29 Mar 2026 - 7:29

score 140 · Answer 7 · 2026-04-01 10:01:30

140

Views

Consequences of $f$ is injective and $g$ is surjective in the following sequence?

Published on 01 Apr 2026 - 10:01

score 438 · Answer 8 · 2022-01-29 16:19:59

438

Views

Let $G = \langle a\rangle$ be a group of order $n$. If $H$ is a subgroup of $G$ and $|H|=m$ divides $n$, then $H = \langle a^\frac{n}{m}\rangle$.

Published on 29 Jan 2022 - 16:19

score 533 · Answer 9 · 2022-01-29 17:50:53

533

Views

Cycles of Powers of $2^n \bmod p$

Published on 29 Jan 2022 - 17:50

score 577 · Answer 10 · 2022-01-31 04:50:01

577

Views

Prove that $\mathbb{Z} \times\Bbb Z_2$ and $\mathbb{Z}$ are not isomorphic.

Published on 31 Jan 2022 - 4:50

score 31 · Answer 11 · 2026-03-29 07:29:23

31

Views

number of generators of a quotient group.

Published on 29 Mar 2026 - 7:29

score 512 · Answer 12 · 2022-02-02 21:46:06

512

Views

Every non trivial subgroup of an infinite cyclic group is infinite

Published on 02 Feb 2022 - 21:46

score 47 · Answer 13 · 2026-03-28 20:14:57

47

Views

A direct product $G=\mathbb{Z}_4\times\mathbb{Z}_4\times\mathbb{Z}_4\times\mathbb{Z}_4$ of the cyclic group $\mathbb{Z}_4$ of order $4$.

Published on 28 Mar 2026 - 20:14

score 423 · Answer 14 · 2026-03-29 11:42:59

423

Views

Prove that the groups $D_6$ and $\mathbb{Z}_6$ are isomorphic

Published on 29 Mar 2026 - 11:42

score 79 · Answer 15 · 2022-02-04 20:13:22

79

Views

Let $G$ be cyclic of order $n$. Let $m\in\Bbb Z,m\leq n$. Find the number of subgroups of $G$ that have order $m$. What happens if $m\nmid n$?

Published on 04 Feb 2022 - 20:13

List Question

Confusion about the last step of this proof of " Every subgroup of a cyclic group is cyclic":does not subcase $2.2$ contradict the desired conclusion

Let $G$ be a abelian group such that $|G| = 2p$ and $p$ Is a odd prime number. Prove $G$ is a cyclic group.

Does this contradict my definition of "cyclic"?

Question about "Quotient Group of Cyclic Group is Cyclic"

Asking for clarification in a group theory proof

Groups of order $16$ with a cyclic quotient of order $4$

Consequences of $f$ is injective and $g$ is surjective in the following sequence?

Let $G = \langle a\rangle$ be a group of order $n$. If $H$ is a subgroup of $G$ and $|H|=m$ divides $n$, then $H = \langle a^\frac{n}{m}\rangle$.

Cycles of Powers of $2^n \bmod p$

Prove that $\mathbb{Z} \times\Bbb Z_2$ and $\mathbb{Z}$ are not isomorphic.

number of generators of a quotient group.

Every non trivial subgroup of an infinite cyclic group is infinite

A direct product $G=\mathbb{Z}_4\times\mathbb{Z}_4\times\mathbb{Z}_4\times\mathbb{Z}_4$ of the cyclic group $\mathbb{Z}_4$ of order $4$.

Prove that the groups $D_6$ and $\mathbb{Z}_6$ are isomorphic

Let $G$ be cyclic of order $n$. Let $m\in\Bbb Z,m\leq n$. Find the number of subgroups of $G$ that have order $m$. What happens if $m\nmid n$?

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