List questions from quotient-group

Published on 28 Jul 2021 - 7:28

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Topological cone using cosets

Published on 28 Jul 2021 - 13:49

57

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If $H\le G$ for an abelian group $G$, then $r_p(H)+r_p(G/H)\ge r_p(G)$, where $r_p(K)$ is the $p$-rank of $K$.

Published on 29 Jul 2021 - 17:03

82

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Does a group morphism factor through a quotient group?

Published on 31 Jul 2021 - 14:54

106

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For a group $G$, $N\unlhd G$, $G/N\cong\Bbb{Z}/a\Bbb{Z}$ and $N\cong\Bbb{Z}/b\Bbb{Z}$, where $b<a$ and $(b,a)=1$, show $G$ is abelian.

Published on 06 Aug 2021 - 1:40

201

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Central product isomorphism: $Z_4 * Q_8 \cong Z_4 * D_8$

Published on 28 Mar 2026 - 13:11

66

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Quotient Group of Stabilizer and Larger (probably) Normal Subgroup

Published on 15 Aug 2021 - 14:41

67

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Properties of $\Bbb{Q}/n\Bbb{Z}$

Published on 17 Aug 2021 - 14:34

119

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Algebraic number theory - finiteness of quotient

Published on 23 Feb 2026 - 13:03

91

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Proving quotient of $\mathcal{O}_K $ with ideal $I$ is finite.

Published on 23 Feb 2026 - 13:03

359

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Proof of Dedekind-Kummer theorem

Published on 23 Feb 2026 - 13:06

115

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We have $N\unlhd G$, a cyclic subgroup of order $n$, $G/N$ cyclic group of order $m$ s.t. $\gcd(m,\phi(n))=1$. Show $G$ is abelian.

Published on 23 Aug 2021 - 4:40

97

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Given some group $H$, can we find a group $G\supset H$ with arbitrary $[G:H]$?

Published on 23 Aug 2021 - 8:28

127

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Relations from quotient of free product

Published on 26 Mar 2026 - 4:34

107

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Faithful action on quotient by center

Published on 25 Aug 2021 - 15:23

List Question

If $G$ is finite abelian group and $H$ is a subgroup. Show $\exists K\le G$ such that $G/K\cong H$.

Topological cone using cosets

If $H\le G$ for an abelian group $G$, then $r_p(H)+r_p(G/H)\ge r_p(G)$, where $r_p(K)$ is the $p$-rank of $K$.

Does a group morphism factor through a quotient group?

For a group $G$, $N\unlhd G$, $G/N\cong\Bbb{Z}/a\Bbb{Z}$ and $N\cong\Bbb{Z}/b\Bbb{Z}$, where $b<a$ and $(b,a)=1$, show $G$ is abelian.

Central product isomorphism: $Z_4 * Q_8 \cong Z_4 * D_8$

Quotient Group of Stabilizer and Larger (probably) Normal Subgroup

Properties of $\Bbb{Q}/n\Bbb{Z}$

Algebraic number theory - finiteness of quotient

Proving quotient of $\mathcal{O}_K $ with ideal $I$ is finite.

Proof of Dedekind-Kummer theorem

We have $N\unlhd G$, a cyclic subgroup of order $n$, $G/N$ cyclic group of order $m$ s.t. $\gcd(m,\phi(n))=1$. Show $G$ is abelian.

Given some group $H$, can we find a group $G\supset H$ with arbitrary $[G:H]$?

Relations from quotient of free product

Faithful action on quotient by center

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