List questions from quotient-group

Published on 15 Apr 2026 - 7:19

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presentation of amalgamated sum as a quotient of the direct sum

Published on 29 Apr 2026 - 12:26

171

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If $H \trianglelefteq G$ and $H \subseteq G' \leq G$ then $(G' \trianglelefteq G) \Leftrightarrow (G'/H \trianglelefteq G/H)$

Published on 22 Apr 2026 - 9:29

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Proof verification: If group $G$ is abelian, then quotient group $G/H$ is abelian.

Published on 22 Apr 2026 - 9:28

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If group $G$ is cyclic, then quotient group $G/H$ is cyclic.

Published on 13 Apr 2026 - 22:09

87

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Notational confusion about HNN-extensions: $G=K \ast_{H,t}$.

Published on 07 May 2026 - 1:54

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Is $\Bbb R/\Bbb Z$ isomorphic to $\Bbb R/2\Bbb Z$?

Published on 13 Apr 2026 - 14:46

163

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Quotient group of $D(2,3,7)$ under the Klein Quartic

Published on 29 Apr 2026 - 12:54

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Order of element in a group

Published on 13 Apr 2026 - 6:06

338

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$H$ and $K$ are subgroups of $G$ and $H$ normalizes $K$. Is $H/K$ a group?

Published on 12 Apr 2026 - 11:11

50

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Abelian group quotient computation

Published on 15 Apr 2026 - 14:36

887

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Let $G$ be a finite group such that $H$ is normal in $G$ and $G/H$ has order $7$ then is $G \cong H \times G/H?$

Published on 15 Apr 2026 - 3:32

126

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About the group structure of the quotient $G/H$, where $H$ is a normal subgroup.

Published on 09 Apr 2026 - 13:07

840

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Between the center of a quotient group and the total center

Published on 14 Apr 2026 - 22:29

561

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Abelianity and quotients

Published on 12 Apr 2026 - 12:30

List Question

An exercise for a subring with finite index.

presentation of amalgamated sum as a quotient of the direct sum

If $H \trianglelefteq G$ and $H \subseteq G' \leq G$ then $(G' \trianglelefteq G) \Leftrightarrow (G'/H \trianglelefteq G/H)$

Proof verification: If group $G$ is abelian, then quotient group $G/H$ is abelian.

If group $G$ is cyclic, then quotient group $G/H$ is cyclic.

Notational confusion about HNN-extensions: $G=K \ast_{H,t}$.

Is $\Bbb R/\Bbb Z$ isomorphic to $\Bbb R/2\Bbb Z$?

Quotient group of $D(2,3,7)$ under the Klein Quartic

Order of element in a group

$H$ and $K$ are subgroups of $G$ and $H$ normalizes $K$. Is $H/K$ a group?

Abelian group quotient computation

Let $G$ be a finite group such that $H$ is normal in $G$ and $G/H$ has order $7$ then is $G \cong H \times G/H?$

About the group structure of the quotient $G/H$, where $H$ is a normal subgroup.

Between the center of a quotient group and the total center

Abelianity and quotients

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