Question

Generalization of the well-known commutator relation

score 108 · Answer 1 · 2026-04-17 04:48:43

108

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Generalization of the well-known commutator relation

Published on 17 Apr 2026 - 4:48

score 195 · Answer 2 · 2026-04-29 12:52:28

195

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

Published on 29 Apr 2026 - 12:52

score 2.9k · Answer 3 · 2026-04-13 10:22:29

2.9k

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

Published on 13 Apr 2026 - 10:22

score 5.5k · Answer 4 · 2026-04-10 11:22:59

5.5k

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

Published on 10 Apr 2026 - 11:22

score 95 · Answer 5 · 2026-04-15 19:27:53

95

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Minimal normal subgroup?

Published on 15 Apr 2026 - 19:27

score 64 · Answer 6 · 2026-04-16 20:34:31

64

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

Published on 16 Apr 2026 - 20:34

score 108 · Answer 7 · 2026-04-10 23:02:47

108

Views

Is the specific group abelian?

Published on 10 Apr 2026 - 23:02

score 75 · Answer 8 · 2026-04-29 12:51:09

75

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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 29 Apr 2026 - 12:51

score 291 · Answer 9 · 2026-04-13 03:57:40

291

Views

Subset is normal subgroup iff its cosets inherit natural composition

Published on 13 Apr 2026 - 3:57

score 840 · Answer 10 · 2026-04-15 00:26:55

840

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 15 Apr 2026 - 0:26

score 135 · Answer 11 · 2026-04-11 01:33:16

135

Views

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

Published on 11 Apr 2026 - 1:33

score 292 · Answer 12 · 2026-04-15 03:14:41

292

Views

Commutator of the semidirect product

Published on 15 Apr 2026 - 3:14

score 51 · Answer 13 · 2026-04-15 06:15:43

51

Views

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

Published on 15 Apr 2026 - 6:15

score 80 · Answer 14 · 2026-04-17 12:52:37

80

Views

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

Published on 17 Apr 2026 - 12:52

score 87 · Answer 15 · 2026-04-16 01:55:20

87

Views

Normal subgroups with an additional property

Published on 16 Apr 2026 - 1:55

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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