Question

Generalization of the well-known commutator relation

score 104 · Answer 1 · 2018-03-11 16:01:05

104

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Generalization of the well-known commutator relation

Published on 11 Mar 2018 - 16:01

score 186 · Answer 2 · 2026-03-23 00:32:05

186

Views

Prove or disprove: If $H$ is normal in $G$ and $H$ and $G/H$ are abelian, then $G$ is abelian.

Published on 23 Mar 2026 - 0:32

score 2.9k · Answer 3 · 2018-03-12 01:12:05

2.9k

Views

If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$.

Published on 12 Mar 2018 - 1:12

score 5.5k · Answer 4 · 2018-03-12 04:00:45

5.5k

Views

If $G$ has exactly one subgroup $H$ of order $k$, prove that $H$ is normal in $G$.

Published on 12 Mar 2018 - 4:00

score 90 · Answer 5 · 2018-03-13 16:34:32

90

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Minimal normal subgroup?

Published on 13 Mar 2018 - 16:34

score 61 · Answer 6 · 2018-03-13 17:51:27

61

Views

Let $G= \{ z \in \mathbb{C} \ \ | \ \ az^{n}=b \}, a \in \mathbb{C^{*}}, b \in \mathbb{C}$.

Published on 13 Mar 2018 - 17:51

score 104 · Answer 7 · 2026-03-25 04:36:05

104

Views

Is the specific group abelian?

Published on 25 Mar 2026 - 4:36

score 67 · Answer 8 · 2026-03-23 09:05:31

67

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Let $G = \mathbb{Z}_{512} \times \mathbb{Z}_{1729}$ and let $H = <([0],[1])>$. Show that $G/H$ is isomorphic to $\mathbb{Z}_{512}$.

Published on 23 Mar 2026 - 9:05

score 288 · Answer 9 · 2018-03-14 14:40:22

288

Views

Subset is normal subgroup iff its cosets inherit natural composition

Published on 14 Mar 2018 - 14:40

score 838 · Answer 10 · 2026-03-25 07:46:04

838

Views

Show that for homomorphism $\phi:G\to H$, if $G_{1}$ is normal in $G$, then $\phi(G_{1})$ is normal in $H$.

Published on 25 Mar 2026 - 7:46

score 132 · Answer 11 · 2018-03-16 15:54:02

132

Views

Let H = ⟨R n ⟩. Show that H is normal in D2n.

Published on 16 Mar 2018 - 15:54

score 289 · Answer 12 · 2026-03-25 06:11:58

289

Views

Commutator of the semidirect product

Published on 25 Mar 2026 - 6:11

score 49 · Answer 13 · 2026-03-24 20:42:08

49

Views

Showing that if $N\triangleleft G$ and $U\triangleleft H< G$ then $NU\triangleleft NH$.

Published on 24 Mar 2026 - 20:42

score 75 · Answer 14 · 2018-03-18 22:09:38

75

Views

If then statement regrading definition of lognormal distribution and the inverse of that statement?

Published on 18 Mar 2018 - 22:09

score 83 · Answer 15 · 2018-03-21 11:30:01

83

Views

Normal subgroups with an additional property

Published on 21 Mar 2018 - 11:30

List Question

Generalization of the well-known commutator relation

Prove or disprove: If $H$ is normal in $G$ and $H$ and $G/H$ are abelian, then $G$ is abelian.

If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$.

If $G$ has exactly one subgroup $H$ of order $k$, prove that $H$ is normal in $G$.

Minimal normal subgroup?

Let $G= \{ z \in \mathbb{C} \ \ | \ \ az^{n}=b \}, a \in \mathbb{C^{*}}, b \in \mathbb{C}$.

Is the specific group abelian?

Let $G = \mathbb{Z}_{512} \times \mathbb{Z}_{1729}$ and let $H = <([0],[1])>$. Show that $G/H$ is isomorphic to $\mathbb{Z}_{512}$.

Subset is normal subgroup iff its cosets inherit natural composition

Show that for homomorphism $\phi:G\to H$, if $G_{1}$ is normal in $G$, then $\phi(G_{1})$ is normal in $H$.

Let H = ⟨R n ⟩. Show that H is normal in D2n.

Commutator of the semidirect product

Showing that if $N\triangleleft G$ and $U\triangleleft H< G$ then $NU\triangleleft NH$.

If then statement regrading definition of lognormal distribution and the inverse of that statement?

Normal subgroups with an additional property

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