List questions from quotient-group

Published on 20 Aug 2023 - 14:39

154

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Composition series with non isomorphic quotients

Published on 31 Aug 2023 - 11:46

135

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Quotient group by two isomorphic groups

Published on 13 Sep 2023 - 13:32

44

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Stallings' Theorem

Published on 19 Sep 2023 - 1:26

65

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$G/H \cong \mathbb{Z}$ implies existence of $K \leq G$ s.t. $K \cap H = 1$ and $HK = G$

Published on 19 Sep 2023 - 12:22

62

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Finding all the possible orders of elements in a quotient group

Published on 20 Sep 2023 - 10:22

77

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For group $G,H$, $f: G \to H$ be an homomorphism, and $N$ be a normal subgroup of $G$, $\frac{G}{N} \cong Im(f) \implies N \cong Ker(f)?$.

Published on 27 Sep 2023 - 1:53

59

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Quotient group isomophic to $\mathbb{Z}$

Published on 03 Oct 2023 - 10:38

62

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Quotient Ring example issue

Published on 21 Mar 2026 - 20:25

49

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If every quotient group of a group G by non-trivial normal subgroups is abelian, G is abelian

Published on 09 Oct 2023 - 19:50

63

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If every quotient group of G by non-trivial normal subgroups are finite, then G is finite

Published on 09 Oct 2023 - 20:40

106

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Pontryagin duality and quotient groups

Published on 11 Oct 2023 - 17:26

67

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Proving that $A_4/V_4$ can be generated by $\sigma V_4$ where $\sigma$ is a 3-cycle

Published on 18 Oct 2023 - 0:51

102

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True/false: If $N\unlhd G$, then for any homomorphism $f:G\to G/N$, the kernel of $f$ contains $N$.

Published on 21 Oct 2023 - 21:05

183

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What are the elements of the group $15 \mathbb Z/ 15 \mathbb Z$?

Published on 25 Oct 2023 - 8:31

List Question

Openness of canonical projection of quotient topological group

Composition series with non isomorphic quotients

Quotient group by two isomorphic groups

Stallings' Theorem

$G/H \cong \mathbb{Z}$ implies existence of $K \leq G$ s.t. $K \cap H = 1$ and $HK = G$

Finding all the possible orders of elements in a quotient group

For group $G,H$, $f: G \to H$ be an homomorphism, and $N$ be a normal subgroup of $G$, $\frac{G}{N} \cong Im(f) \implies N \cong Ker(f)?$.

Quotient group isomophic to $\mathbb{Z}$

Quotient Ring example issue

If every quotient group of a group G by non-trivial normal subgroups is abelian, G is abelian

If every quotient group of G by non-trivial normal subgroups are finite, then G is finite

Pontryagin duality and quotient groups

Proving that $A_4/V_4$ can be generated by $\sigma V_4$ where $\sigma$ is a 3-cycle

True/false: If $N\unlhd G$, then for any homomorphism $f:G\to G/N$, the kernel of $f$ contains $N$.

What are the elements of the group $15 \mathbb Z/ 15 \mathbb Z$?

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