List questions from normal-subgroups

Published on 06 Mar 2017 - 19:15

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A normal subgroup is the union of conjugacy classes.

Published on 07 Mar 2017 - 11:16

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Subgroup of the free group on 3 generators

Published on 27 Mar 2026 - 0:04

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$G$ group of order $36$, $H\le G$ of order $9$. Show that either $H\unlhd G$ or there is $K\le H$ of order $3$, $K\unlhd G$.

Published on 28 Mar 2026 - 23:33

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Is it true that cyclic subgroups are always normal?

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The Commutator Subgroup is Normal.

Published on 13 Mar 2017 - 14:14

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Why $N_G(N_G(H)) = N_G(H)$ for some subgroup H < G.

Published on 15 Mar 2017 - 2:48

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Finding the kernel of $\phi$ of applying the First Isomorphism Theorem

Published on 29 Mar 2026 - 20:55

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Are there necessary and sufficient conditions for any group to have a maximal normal subgroup?

Published on 25 Mar 2026 - 4:41

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Commutator subgroup and subgroup generated by square.

Published on 18 Mar 2017 - 14:31

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Proving something is a normal subgroup?

Published on 18 Mar 2017 - 17:07

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Does $GL_2(\Bbb Z_3)$ have a normal subgroup of order 8, or 16?

Published on 25 Mar 2026 - 17:39

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$H_1$ and $H_2$ normal subgroups of $G$, $f(g)=(gH_1, gH_2)$ and $G.C.D.(|G/H_1|,|G/H_2|)=1$ then $f$ is epimorphism

Published on 29 Mar 2026 - 22:33

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How the quotient group of following matrix group looks like?

Published on 26 Mar 2026 - 19:19

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How do you prove this question about groups?

Published on 23 Mar 2017 - 8:31

List Question

Proving Normal Subgroups

A normal subgroup is the union of conjugacy classes.

Subgroup of the free group on 3 generators

$G$ group of order $36$, $H\le G$ of order $9$. Show that either $H\unlhd G$ or there is $K\le H$ of order $3$, $K\unlhd G$.

Is it true that cyclic subgroups are always normal?

The Commutator Subgroup is Normal.

Why $N_G(N_G(H)) = N_G(H)$ for some subgroup H < G.

Finding the kernel of $\phi$ of applying the First Isomorphism Theorem

Are there necessary and sufficient conditions for any group to have a maximal normal subgroup?

Commutator subgroup and subgroup generated by square.

Proving something is a normal subgroup?

Does $GL_2(\Bbb Z_3)$ have a normal subgroup of order 8, or 16?

$H_1$ and $H_2$ normal subgroups of $G$, $f(g)=(gH_1, gH_2)$ and $G.C.D.(|G/H_1|,|G/H_2|)=1$ then $f$ is epimorphism

How the quotient group of following matrix group looks like?

How do you prove this question about groups?

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