List questions from quotient-group

Published on 26 Mar 2026 - 7:56

35

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Is it true that $\mathbb{R}^{d}/n\mathbb{Z}^{d} = n(\mathbb{S}^{1})^{d}$?

Published on 25 May 2020 - 22:37

40

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G is a commutative group of order 2*N, how to prove G has a N-order quotient group?

Published on 26 May 2020 - 1:23

381

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prove that the unit circle is isomorphic to the quotient group $\Bbb R/K$, where $K$ is a normal subgroup of $(\Bbb R, +)$

Published on 26 May 2020 - 15:08

70

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Representing a group as a quotient of a free group

Published on 30 May 2020 - 8:34

179

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On the ring $\frac{\mathbb{Q}[x]}I$ , where $I=\langle x^2-x\rangle$

Published on 31 May 2020 - 12:21

393

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Algebraic Extensions of Z_7 with polynomials?

Published on 25 Mar 2026 - 16:01

450

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For G and H groups, show that (G×{e})◃(G×H), then show that the quotient (G×H)/(G×{e}) is isomorphic to H.

Published on 01 Jun 2020 - 1:45

60

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Differences between polynomial quotient rings $\mathbb{Z}_m[x]/(x^n+1)$ and $\mathbb{Z}_m[x]/(x^n-1)$

Published on 01 Jun 2020 - 17:23

32

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Elements of $\mathbb{F}_7^/\mathbb{F}_7^{3}$

Published on 02 Jun 2020 - 12:27

578

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Is a quotient group of a non-cyclic group again a non-cyclic group?

Published on 03 Jun 2020 - 15:44

104

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Finding isomorphism between two groups

Published on 03 Jun 2020 - 20:59

173

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Identifying quotient groups of matrices

Published on 05 Jun 2020 - 0:08

86

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Finding the order of $(1, 1) + \langle(2, 2)\rangle$ in the factor group $\mathbb{Z} \times \mathbb{Z} / \langle (2, 2)\rangle$

Published on 06 Jun 2020 - 23:41

442

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Size of quotient groups

Published on 07 Jun 2020 - 14:52

List Question

Word problem and quotient group

Is it true that $\mathbb{R}^{d}/n\mathbb{Z}^{d} = n(\mathbb{S}^{1})^{d}$?

G is a commutative group of order 2*N, how to prove G has a N-order quotient group?

prove that the unit circle is isomorphic to the quotient group $\Bbb R/K$, where $K$ is a normal subgroup of $(\Bbb R, +)$

Representing a group as a quotient of a free group

On the ring $\frac{\mathbb{Q}[x]}I$ , where $I=\langle x^2-x\rangle$

Algebraic Extensions of Z_7 with polynomials?

For G and H groups, show that (G×{e})◃(G×H), then show that the quotient (G×H)/(G×{e}) is isomorphic to H.

Differences between polynomial quotient rings $\mathbb{Z}_m[x]/(x^n+1)$ and $\mathbb{Z}_m[x]/(x^n-1)$

Elements of $\mathbb{F}_7^/\mathbb{F}_7^{3}$

Is a quotient group of a non-cyclic group again a non-cyclic group?

Finding isomorphism between two groups

Identifying quotient groups of matrices

Finding the order of $(1, 1) + \langle(2, 2)\rangle$ in the factor group $\mathbb{Z} \times \mathbb{Z} / \langle (2, 2)\rangle$

Size of quotient groups

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