Question

For all $g\in G$, is it true that $gHg^{-1} \subseteq H $ if H is a normal subgroup of G.

score 290 · Answer 1 · 2016-04-30 18:59:43

290

Views

For all $g\in G$, is it true that $gHg^{-1} \subseteq H $ if H is a normal subgroup of G.

Published on 30 Apr 2016 - 18:59

score 1.6k · Answer 2 · 2016-04-30 21:45:36

1.6k

Views

Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.

Published on 30 Apr 2016 - 21:45

score 540 · Answer 3 · 2016-05-01 01:55:22

540

Views

what is the smallest non-abelian finite group which has normal, non-abelian subgroups (plural)

Published on 01 May 2016 - 1:55

score 68 · Answer 4 · 2016-05-03 02:23:29

68

Views

Order $4$ subgroup of alternating group $A_4$

Published on 03 May 2016 - 2:23

score 19.4k · Answer 5 · 2016-05-03 21:19:26

19.4k

Views

Are all normal subgroups Abelian?

Published on 03 May 2016 - 21:19

score 365 · Answer 6 · 2016-05-06 15:51:25

365

Views

Two normal subgroups and isomorphism theorem

Published on 06 May 2016 - 15:51

score 2.6k · Answer 7 · 2026-04-02 18:06:18

2.6k

Views

Normal subgroups of $A_5$ must contain a 3-cycle.

Published on 02 Apr 2026 - 18:06

score 67 · Answer 8 · 2016-05-09 13:20:30

Let $N_i \subseteq G_i$ for $i = 1, ..., n$ be Normal subgroups. Show that $\prod_{i=1}^{n}N_i \subseteq \prod_{i=1}^{n}G_i$ is a Normal subgroup

score 32 · Answer 9 · 2016-05-10 18:34:38

32

Views

Criterion for a group $G$ to be abelian using $Inn(G)$

Published on 10 May 2016 - 18:34

score 151 · Answer 10 · 2016-05-10 19:20:41

151

Views

A Group G is abelian $\Leftrightarrow$ $ Inn(G)$ is a normal subgroup of Sym(G)

Published on 10 May 2016 - 19:20

score 894 · Answer 11 · 2016-05-11 19:52:15

894

Views

Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic

Published on 11 May 2016 - 19:52

score 4k · Answer 12 · 2016-05-13 07:20:18

4k

Views

All subgroups normal $\implies$ abelian group

Published on 13 May 2016 - 7:20

score 3.8k · Answer 13 · 2016-05-14 05:16:23

3.8k

Views

If the intersection of two normal subgroups is trivial, then their elements commute

Published on 14 May 2016 - 5:16

score 244 · Answer 14 · 2016-05-14 09:52:56

244

Views

Groups of order 12 with a normal 3-subgroup contain an element of order 6

Published on 14 May 2016 - 9:52

score 119 · Answer 15 · 2026-03-27 14:22:26

119

Views

Quotient of $G= \left\langle a, b \ \middle|\ a^4, b^2=a^4, aba=b \right\rangle$ by $\langle a^2 \rangle$

Published on 27 Mar 2026 - 14:22

List Question

For all $g\in G$, is it true that $gHg^{-1} \subseteq H $ if H is a normal subgroup of G.

Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.

what is the smallest non-abelian finite group which has normal, non-abelian subgroups (plural)

Order $4$ subgroup of alternating group $A_4$

Are all normal subgroups Abelian?

Two normal subgroups and isomorphism theorem

Normal subgroups of $A_5$ must contain a 3-cycle.

Let $N_i \subseteq G_i$ for $i = 1, ..., n$ be Normal subgroups. Show that $\prod_{i=1}^{n}N_i \subseteq \prod_{i=1}^{n}G_i$ is a Normal subgroup

Criterion for a group $G$ to be abelian using $Inn(G)$

A Group G is abelian $\Leftrightarrow$ $ Inn(G)$ is a normal subgroup of Sym(G)

Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic

All subgroups normal $\implies$ abelian group

If the intersection of two normal subgroups is trivial, then their elements commute

Groups of order 12 with a normal 3-subgroup contain an element of order 6

Quotient of $G= \left\langle a, b \ \middle|\ a^4, b^2=a^4, aba=b \right\rangle$ by $\langle a^2 \rangle$

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