List questions from normal-subgroups

Published on 14 Jul 2015 - 12:43

90

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$H\subseteq G$, $N\triangleleft G$, and showing $|[G:N]|$ is a prime number

Published on 18 Jul 2015 - 1:50

10.9k

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Every normal subgroup is the kernel of some homomorphism

Published on 31 Mar 2026 - 17:49

202

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More Symmetric than the symmetric groups?

Published on 01 Apr 2026 - 11:36

39

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Homomorphic image if smaller fails to exist

Published on 31 Mar 2026 - 14:24

98

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Does $AN/N=A/N$?

Published on 31 Mar 2026 - 14:32

6.3k

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Prove that the 4-group V is normal subgroup of $S_4$ by using isomorphism theorem

Published on 23 Jul 2015 - 5:18

48

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A question about Inner and outer Automorphism

Published on 07 Aug 2015 - 18:07

345

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To show that H,K are sub-groups of G (U36)

Published on 23 Feb 2026 - 15:33

314

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Union of conjugacy classes of $O(n)$ is not a subgroup

Published on 12 Aug 2015 - 10:13

1k

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If $H$ is a subgroup of a group $G$, and $K$ a normal subgroup of $G$, is $H\cap K$ a normal subgroup of $G$?

Published on 13 Aug 2015 - 5:46

1.1k

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Finite normal subgroups of $SO(4)$

Published on 30 Mar 2026 - 6:44

11.1k

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Proof that normalizer and center are subgroups

Published on 23 Aug 2015 - 16:08

252

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prove unique minimal normal subgroup of soluble group by $ P_{G}(M) > M $

Published on 31 Aug 2015 - 15:57

535

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Let $G$ group of order $pq$ where $p,q$ primes.Show that if $G$ contains normal groups $N$ and $K$ with $|N|=p$ and $|K|=q$ then is cyclic

Published on 02 Sep 2015 - 8:25

List Question

show that $\varphi : H \to H /N$ is one-to-one correspondence using kernel

$H\subseteq G$, $N\triangleleft G$, and showing $|[G:N]|$ is a prime number

Every normal subgroup is the kernel of some homomorphism

More Symmetric than the symmetric groups?

Homomorphic image if smaller fails to exist

Does $AN/N=A/N$?

Prove that the 4-group V is normal subgroup of $S_4$ by using isomorphism theorem

A question about Inner and outer Automorphism

To show that H,K are sub-groups of G (U36)

Union of conjugacy classes of $O(n)$ is not a subgroup

If $H$ is a subgroup of a group $G$, and $K$ a normal subgroup of $G$, is $H\cap K$ a normal subgroup of $G$?

Finite normal subgroups of $SO(4)$

Proof that normalizer and center are subgroups

prove unique minimal normal subgroup of soluble group by $ P_{G}(M) > M $

Let $G$ group of order $pq$ where $p,q$ primes.Show that if $G$ contains normal groups $N$ and $K$ with $|N|=p$ and $|K|=q$ then is cyclic

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