List questions from quotient-group

Published on 11 Jun 2019 - 12:27

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Proof that quotient group is cyclic and find its generator

Published on 18 Jun 2019 - 19:34

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Find all Quotient (or Factor) Groups of $D_4$ (Dihedral Group of order $8$)

Published on 20 Jun 2019 - 20:18

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GCD in multivariate polynomial ring and quotient ring

Published on 25 Mar 2026 - 4:37

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Show that a group $G$ so that the order of the quotient group is $| G/C(G) | = 37$ doesn't exist.

Published on 30 Jun 2019 - 11:21

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The quotient in $ \mathbb{Z} _{5} [x] $ by a irreducible polynomial.

Published on 30 Jun 2019 - 19:10

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Let $f(x) =x^3+x+1 \in \mathbb{Q} [x] $. If ideal $I=(f(x)) $, find the inverse of $x^2+x+1$ in quotient $\mathbb{Q} [x] /I$.

Published on 01 Jul 2019 - 14:26

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Quotient group is cyclic or not?

Published on 01 Jul 2019 - 18:54

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If $H$ is a normal subgroup of $S_n$ where $(12)(34)∈ H$, $Sn/H \cong {e}$ or $Sn/H \cong Z/2Z$.

Published on 08 Jul 2019 - 7:06

479

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Set of representatives of coset in quotient group

Published on 09 Jul 2019 - 14:44

314

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pullback of quotient map: injective on group cohomology?

Published on 23 Feb 2026 - 4:49

66

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Subgroups of Quotient Groups

Published on 12 Jul 2019 - 16:54

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Commutator subgroup of Heisenberg group.

Published on 22 Mar 2026 - 2:57

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$[A:B] = [\overline{A}: \overline{B}]$ quotient groups correspondence.

Published on 18 Jul 2019 - 22:21

466

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When the derived (commutator) subgroup is in the center

Published on 20 Jul 2019 - 1:37

List Question

Subgroup automorphisms

Proof that quotient group is cyclic and find its generator

Find all Quotient (or Factor) Groups of $D_4$ (Dihedral Group of order $8$)

GCD in multivariate polynomial ring and quotient ring

Show that a group $G$ so that the order of the quotient group is $| G/C(G) | = 37$ doesn't exist.

The quotient in $ \mathbb{Z} _{5} [x] $ by a irreducible polynomial.

Let $f(x) =x^3+x+1 \in \mathbb{Q} [x] $. If ideal $I=(f(x)) $, find the inverse of $x^2+x+1$ in quotient $\mathbb{Q} [x] /I$.

Quotient group is cyclic or not?

If $H$ is a normal subgroup of $S_n$ where $(12)(34)∈ H$, $Sn/H \cong {e}$ or $Sn/H \cong Z/2Z$.

Set of representatives of coset in quotient group

pullback of quotient map: injective on group cohomology?

Subgroups of Quotient Groups

Commutator subgroup of Heisenberg group.

$[A:B] = [\overline{A}: \overline{B}]$ quotient groups correspondence.

When the derived (commutator) subgroup is in the center

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