List questions from normal-subgroups

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Proving Normal subgroups and abelian

Published on 26 Oct 2014 - 17:38

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Inverses of Subgroups

Published on 28 Oct 2014 - 23:28

122

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Solution verification: $G$ and $G/H$ contain elements of same order

Published on 28 Mar 2026 - 11:53

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Proving the existence of a homomorphism $\overline f:G/H\rightarrow G'$ such that $\overline f \pi = f.$

Published on 30 Oct 2014 - 6:02

50

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Subgroups of the simple groups

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112

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Can subgroups of subgroups be normal?

Published on 01 Nov 2014 - 20:57

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Show that $G/H\cong S_3$

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691

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Largest Normal Subgroup of a Group G

Published on 04 Nov 2014 - 1:53

1k

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How is $S_n$ not simple for $n \geq 3$?

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If the normalizer of a subgroup in a group is equal to the subgroup then is the subgroup abelian?

Published on 07 Nov 2014 - 6:38

337

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T/F questions on $p$-Sylow subgroups and normalizer

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220

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Properties possessed by $H , G/H$ but not G

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436

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Consider $f: \mathbb Z_8 \rightarrow \mathbb Z_4$. List the cosets of the kernel of $f$

Published on 27 Mar 2026 - 13:20

33

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Proof that, if factor groups are equal, then the subgroups are equal

Published on 08 Nov 2014 - 1:25

List Question

Showing the product of two normal subgroups is normal

Proving Normal subgroups and abelian

Inverses of Subgroups

Solution verification: $G$ and $G/H$ contain elements of same order

Proving the existence of a homomorphism $\overline f:G/H\rightarrow G'$ such that $\overline f \pi = f.$

Subgroups of the simple groups

Can subgroups of subgroups be normal?

Show that $G/H\cong S_3$

Largest Normal Subgroup of a Group G

How is $S_n$ not simple for $n \geq 3$?

If the normalizer of a subgroup in a group is equal to the subgroup then is the subgroup abelian?

T/F questions on $p$-Sylow subgroups and normalizer

Properties possessed by $H , G/H$ but not G

Consider $f: \mathbb Z_8 \rightarrow \mathbb Z_4$. List the cosets of the kernel of $f$

Proof that, if factor groups are equal, then the subgroups are equal

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