List questions from normal-subgroups

Published on 07 Nov 2019 - 22:30

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Suppose $aHbH$ is a left coset. Show that $H$ is normal in $G$.

Published on 08 Nov 2019 - 14:29

91

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Locally cyclic quotient and locally cyclic subgroup

Published on 25 Mar 2026 - 19:03

39

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Showing that if $H_1 \unlhd H$ and $G_1 \unlhd G$, then $H_1 \times G_1 \unlhd H \times G $

Published on 26 Mar 2026 - 12:50

201

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Cyclic Group Homomorphisms and Subgroups

Published on 11 Nov 2019 - 17:24

1k

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True or false: If $N$ is a normal subgroup of $G$, then $gng^{-1 }= n$ for all $n \in N$ and $g \in G$. Justify

Published on 27 Mar 2026 - 19:54

540

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Assume $N \triangleleft G$ Prove that if $[G:H]$ is a prime, then $G/N$ is cyclic. prove or disprove the converse of the first statement.

Published on 13 Nov 2019 - 1:47

459

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Relationship between a normal subgroup and a stabilizer

Published on 28 Mar 2026 - 11:42

204

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Normal subgroup fixes every element of a set.

Published on 28 Mar 2026 - 11:42

702

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Prove that a group of order 42 has a non trivial normal subgroup

Published on 16 Nov 2019 - 17:08

47

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Do these assumptions guarantee $HK_1 \neq HK_2$?

Published on 16 Nov 2019 - 23:54

576

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Can $G/H$ be cyclic if $G$ is nonabelian?

Published on 26 Mar 2026 - 4:31

43

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Let $G$ be a group and $g \in G$ have order $2$. Show that $\langle g \rangle \unlhd G \iff g \in Z(G)$.

Published on 18 Nov 2019 - 18:32

192

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Normal subgroups of signed symmetric groups

Published on 28 Mar 2026 - 9:54

66

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Under what assumptions will $M \unlhd G$? ($M$ maximal)

Published on 21 Nov 2019 - 1:37

List Question

What does it mean for complexes of a group to be conjugate?

Suppose $aHbH$ is a left coset. Show that $H$ is normal in $G$.

Locally cyclic quotient and locally cyclic subgroup

Showing that if $H_1 \unlhd H$ and $G_1 \unlhd G$, then $H_1 \times G_1 \unlhd H \times G $

Cyclic Group Homomorphisms and Subgroups

True or false: If $N$ is a normal subgroup of $G$, then $gng^{-1 }= n$ for all $n \in N$ and $g \in G$. Justify

Assume $N \triangleleft G$ Prove that if $[G:H]$ is a prime, then $G/N$ is cyclic. prove or disprove the converse of the first statement.

Relationship between a normal subgroup and a stabilizer

Normal subgroup fixes every element of a set.

Prove that a group of order 42 has a non trivial normal subgroup

Do these assumptions guarantee $HK_1 \neq HK_2$?

Can $G/H$ be cyclic if $G$ is nonabelian?

Let $G$ be a group and $g \in G$ have order $2$. Show that $\langle g \rangle \unlhd G \iff g \in Z(G)$.

Normal subgroups of signed symmetric groups

Under what assumptions will $M \unlhd G$? ($M$ maximal)

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