List questions from quotient-group

Published on 28 Dec 2020 - 13:39

882

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Quotient group of finitely generated group is finitely generated

Published on 30 Dec 2020 - 3:54

104

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Factor group of a free group

Published on 26 Mar 2026 - 23:09

91

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$G$ is cyclic of order $10$, describe all quotients of $G$

Published on 03 Jan 2021 - 12:28

580

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Prove or disprove: If $H$ is a normal subgroup and cyclic and $G/H$ are cyclic, then $G$ is cyclic.

Published on 09 Jan 2021 - 21:04

65

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Group of order $pqrt$

Published on 10 Jan 2021 - 13:35

28

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Efficient way of writing the elements of a quotient group.

Published on 11 Jan 2021 - 17:02

79

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Isomorphism between groups and subgroups.

Published on 13 Jan 2021 - 12:12

123

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Let $H, K \lhd G$, then $G = HK \iff G / (H \cap K) \cong G / H \times G / K$

Published on 27 Mar 2026 - 22:57

78

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Is it surjective because of $K \subset H$?

Published on 13 Jan 2021 - 21:28

204

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Construct a "natural" bijection between homomorphisms with domain $G$ and homomorphisms with a factor group $G/H$ as domain.

Published on 19 Jan 2021 - 19:13

110

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Arbitrary subset of quotient group or ring

Published on 20 Jan 2021 - 4:35

115

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Category Diagram of a Quotient Group

Published on 20 Jan 2021 - 17:21

314

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Is $\mathbb{R/Z}$ isomorphic to $\mathbb{Q/Z}$?

Published on 21 Jan 2021 - 14:44

113

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Size of $ \mathbb{Z}^m/\Lambda$, for $\Lambda \subset \mathbb{Z}^m$

Published on 23 Jan 2021 - 21:11

List Question

Product of groups with "identified" quoteint.

Quotient group of finitely generated group is finitely generated

Factor group of a free group

$G$ is cyclic of order $10$, describe all quotients of $G$

Prove or disprove: If $H$ is a normal subgroup and cyclic and $G/H$ are cyclic, then $G$ is cyclic.

Group of order $pqrt$

Efficient way of writing the elements of a quotient group.

Isomorphism between groups and subgroups.

Let $H, K \lhd G$, then $G = HK \iff G / (H \cap K) \cong G / H \times G / K$

Is it surjective because of $K \subset H$?

Construct a "natural" bijection between homomorphisms with domain $G$ and homomorphisms with a factor group $G/H$ as domain.

Arbitrary subset of quotient group or ring

Category Diagram of a Quotient Group

Is $\mathbb{R/Z}$ isomorphic to $\mathbb{Q/Z}$?

Size of $ \mathbb{Z}^m/\Lambda$, for $\Lambda \subset \mathbb{Z}^m$

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