List questions from quotient-group

Published on 22 Apr 2019 - 16:38

335

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Size of conjugacy class of a quotient group

Published on 23 Apr 2019 - 1:35

842

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Show that if N, K are normal subgroups of a group G, and N contains K then we have: $ G / N \cong (G/K) / (N /K) $

Published on 23 Apr 2019 - 7:27

266

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Orders of the Elements of $D_6/Z(D_6)$

Published on 04 May 2019 - 2:03

71

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Groups, subgroups and quotient groups

Published on 04 May 2019 - 8:54

119

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How to make quotient group operation well-defined

Published on 07 May 2019 - 17:02

57

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Elementary question on quotient group construction

Published on 19 May 2019 - 19:01

100

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Basic theorem for solvable groups not true for nilpotent groups - counterexample.

Published on 25 Mar 2026 - 4:44

778

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If $G$ is a non-abelian finite group, then $|Z(G)| \leq \frac {1}{4} |G|$

Published on 26 May 2019 - 1:34

1.9k

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When is a quotient group $G/H$ abelian?

Published on 26 May 2019 - 2:49

334

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show that if $G/K, G/N$ are solvable then $G/(K \cap N)$ is also solvable

Published on 25 Mar 2026 - 6:06

84

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Quotient group izomorphic with torus

Published on 04 Jun 2019 - 11:35

92

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When quotient group is cyclic?

Published on 08 Jun 2019 - 14:17

148

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Let $G$ be a group of order $8$ and $y$ be an element of $G$ of order $4$. Prove that $y^2 \in Z(G)$

Published on 09 Jun 2019 - 1:58

40

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Explicit form of $\ker ( \mathbb{Q}/\mathbb{Z} \xrightarrow{\cdot 3} \mathbb{Q}/\mathbb{Z} )$

Published on 09 Jun 2019 - 12:38

List Question

Quotient group of dihedral group

Size of conjugacy class of a quotient group

Show that if N, K are normal subgroups of a group G, and N contains K then we have: $ G / N \cong (G/K) / (N /K) $

Orders of the Elements of $D_6/Z(D_6)$

Groups, subgroups and quotient groups

How to make quotient group operation well-defined

Elementary question on quotient group construction

Basic theorem for solvable groups not true for nilpotent groups - counterexample.

If $G$ is a non-abelian finite group, then $|Z(G)| \leq \frac {1}{4} |G|$

When is a quotient group $G/H$ abelian?

show that if $G/K, G/N$ are solvable then $G/(K \cap N)$ is also solvable

Quotient group izomorphic with torus

When quotient group is cyclic?

Let $G$ be a group of order $8$ and $y$ be an element of $G$ of order $4$. Prove that $y^2 \in Z(G)$

Explicit form of $\ker ( \mathbb{Q}/\mathbb{Z} \xrightarrow{\cdot 3} \mathbb{Q}/\mathbb{Z} )$

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