Question

Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.

score 3.3k · Answer 1 · 2016-11-04 19:42:16

3.3k

Views

Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.

Published on 04 Nov 2016 - 19:42

score 862 · Answer 2 · 2026-03-26 23:09:52

862

Views

Groups in derived series are normal in the whole group

Published on 26 Mar 2026 - 23:09

score 3.5k · Answer 3 · 2016-11-05 20:04:43

3.5k

Views

Relation between the centralizer and the conjugacy class!

Published on 05 Nov 2016 - 20:04

score 4.1k · Answer 4 · 2016-11-05 21:22:50

4.1k

Views

Looking for a nice example for normal subgroups

Published on 05 Nov 2016 - 21:22

score 331 · Answer 5 · 2026-03-26 11:18:11

331

Views

Looking for a proof that if a normal subgroup of $Sym(\mathbb N)$ has an element of infinite order then it is the whole group

Published on 26 Mar 2026 - 11:18

score 185 · Answer 6 · 2016-11-07 20:59:31

185

Views

A subgroup is normal iff it is invariant under every inner automorphism. How to prove that An⊴Sn.

Published on 07 Nov 2016 - 20:59

score 174 · Answer 7 · 2016-11-08 00:46:28

174

Views

Show that $A_n$ is a normal subgroup of $S_n$ by defining a homomorphism from $S_n$ to $Z_2$ and showing that $A_n$ is its kernel.

Published on 08 Nov 2016 - 0:46

score 25 · Answer 8 · 2016-11-09 01:59:16

25

Views

Does conjugacy persevere being subgroup of each others

Published on 09 Nov 2016 - 1:59

score 28 · Answer 9 · 2016-11-09 20:52:48

28

Views

Inclusion or equality - Conjugation (Groups)

Published on 09 Nov 2016 - 20:52

score 53 · Answer 10 · 2016-11-12 19:39:40

53

Views

Proving a custom subgroup $HK$ is closed.

Published on 12 Nov 2016 - 19:39

score 38 · Answer 11 · 2016-11-12 22:15:02

38

Views

Proof that a specific subgroup $S$ is normal

Published on 12 Nov 2016 - 22:15

score 681 · Answer 12 · 2026-03-26 19:19:41

681

Views

Intersection of elements of a internal direct product is the identity

Published on 26 Mar 2026 - 19:19

score 56 · Answer 13 · 2016-11-16 16:51:55

56

Views

Normal groups in abstract algebra

Published on 16 Nov 2016 - 16:51

score 387 · Answer 14 · 2016-11-16 18:26:56

387

Views

An exercise about normal subgroups

Published on 16 Nov 2016 - 18:26

score 87 · Answer 15 · 2016-11-17 22:59:42

87

Views

Consecutive Galois extensions

Published on 17 Nov 2016 - 22:59

List Question

Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.

Groups in derived series are normal in the whole group

Relation between the centralizer and the conjugacy class!

Looking for a nice example for normal subgroups

Looking for a proof that if a normal subgroup of $Sym(\mathbb N)$ has an element of infinite order then it is the whole group

A subgroup is normal iff it is invariant under every inner automorphism. How to prove that An⊴Sn.

Show that $A_n$ is a normal subgroup of $S_n$ by defining a homomorphism from $S_n$ to $Z_2$ and showing that $A_n$ is its kernel.

Does conjugacy persevere being subgroup of each others

Inclusion or equality - Conjugation (Groups)

Proving a custom subgroup $HK$ is closed.

Proof that a specific subgroup $S$ is normal

Intersection of elements of a internal direct product is the identity

Normal groups in abstract algebra

An exercise about normal subgroups

Consecutive Galois extensions

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