Question

How to show $\forall g \in G, gHg^{-1} = H \Leftrightarrow \forall g \in G, gHg^{-1} \subseteq H$?

score 581 · Answer 1 · 2013-09-21 02:08:16

581

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How to show $\forall g \in G, gHg^{-1} = H \Leftrightarrow \forall g \in G, gHg^{-1} \subseteq H$?

Published on 21 Sep 2013 - 2:08

score 1.9k · Answer 2 · 2013-10-10 07:36:44

1.9k

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A question based on Normal Subgroups

Published on 10 Oct 2013 - 7:36

score 14.3k · Answer 3 · 2013-10-19 15:32:17

14.3k

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Example of a Subgroup That Is Not Normal

Published on 19 Oct 2013 - 15:32

score 7.8k · Answer 4 · 2013-10-22 13:40:10

7.8k

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Non abelian group with normal subgroup

Published on 22 Oct 2013 - 13:40

score 2.7k · Answer 5 · 2026-04-01 18:49:52

2.7k

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Subgroups containing kernel of group morphism to an abelian group are normal.

Published on 01 Apr 2026 - 18:49

score 117 · Answer 6 · 2013-11-02 08:02:33

117

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Prove that $N \setminus Z(G)\neq \langle e \rangle$.

Published on 02 Nov 2013 - 8:02

score 5.4k · Answer 7 · 2013-11-08 16:29:35

5.4k

Views

Let G be a group. If H is a normal subgroup in G, and K is a normal subgroup of H, when is K a normal subgroup of G?

Published on 08 Nov 2013 - 16:29

score 62 · Answer 8 · 2013-11-10 02:53:47

62

Views

Group Theory (basic)

Published on 10 Nov 2013 - 2:53

score 1.8k · Answer 9 · 2013-11-11 01:17:04

1.8k

Views

Let G be cyclic and let H be a subgroup of G. Show that G/H is cyclic.

Published on 11 Nov 2013 - 1:17

score 288 · Answer 10 · 2013-11-11 22:49:18

288

Views

isomorphism between two factor groups

Published on 11 Nov 2013 - 22:49

score 2.3k · Answer 11 · 2013-11-14 07:17:45

2.3k

Views

Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.

Published on 14 Nov 2013 - 7:17

score 61 · Answer 12 · 2013-11-14 10:27:47

61

Views

Question about proving something about subgroup

Published on 14 Nov 2013 - 10:27

score 35 · Answer 13 · 2013-11-14 16:35:18

35

Views

Question about describing a sub-group of $S_{\mathbb{R}}$

Published on 14 Nov 2013 - 16:35

score 146 · Answer 14 · 2013-11-15 08:22:08

146

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$ G/N$ has an element of order $m$ so, $G$ also has an element of order $m$

Published on 15 Nov 2013 - 8:22

score 1.3k · Answer 15 · 2013-11-17 05:49:21

1.3k

Views

find all the members of A4/K

Published on 17 Nov 2013 - 5:49

List Question

How to show $\forall g \in G, gHg^{-1} = H \Leftrightarrow \forall g \in G, gHg^{-1} \subseteq H$?

A question based on Normal Subgroups

Example of a Subgroup That Is Not Normal

Non abelian group with normal subgroup

Subgroups containing kernel of group morphism to an abelian group are normal.

Prove that $N \setminus Z(G)\neq \langle e \rangle$.

Let G be a group. If H is a normal subgroup in G, and K is a normal subgroup of H, when is K a normal subgroup of G?

Group Theory (basic)

Let G be cyclic and let H be a subgroup of G. Show that G/H is cyclic.

isomorphism between two factor groups

Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.

Question about proving something about subgroup

Question about describing a sub-group of $S_{\mathbb{R}}$

$ G/N$ has an element of order $m$ so, $G$ also has an element of order $m$

find all the members of A4/K

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