List questions from quotient-group

Published on 08 Jun 2023 - 16:31

165

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If every element of $G/H$ has a square root and every element of $H$ has a square root, then every element of $G$ has a square root.

Published on 11 Jun 2023 - 13:30

71

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The factor group $\mathbb{R} / \mathbb{Z}$ under addition has an infinite number of elements of order 4

Published on 26 Mar 2026 - 17:32

208

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Is every finite simple group a quotient of a braid group?

Published on 25 Mar 2026 - 10:57

38

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Isomorphism between isomorphic abelian groups quotiented by isomorphic subgroups

Published on 06 Jul 2023 - 7:05

103

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Writing a quotient group as a product of cyclic groups

Published on 26 Mar 2026 - 22:57

88

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Meaning of factorization of groups

Published on 28 Jul 2023 - 2:44

59

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Element in a coset whose order's prime divisors are those of the order of the coset

Published on 30 Jul 2023 - 20:56

60

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What is meant by the phrase "but the identity in a quotient group is the subgroup" in this Abstract Algebra proof?

Published on 02 Aug 2023 - 19:44

24

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2-groups with abelianization of type (2,2)

Published on 26 Mar 2026 - 6:25

123

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Is it always $|G:gG|=1$ where $G$ is a group and $g \in G$?

Published on 09 Aug 2023 - 14:42

164

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Elements of $\mathbb{Z}_6 / \mathbb{Z}_2$

Published on 13 Aug 2023 - 19:01

79

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Quotient group with $\mathbb{Z}_2$ and $\mathbb{Z}_4$

Published on 13 Aug 2023 - 20:24

66

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Subgroups of self dual groups

Published on 26 Mar 2026 - 6:19

69

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Quotient of the group $\mathbb{Z}^2 \oplus \mathbb{Z} ^2 \oplus \mathbb{Z} ^2$

Published on 14 Aug 2023 - 11:01

List Question

The abelianizer functor is not faithful

If every element of $G/H$ has a square root and every element of $H$ has a square root, then every element of $G$ has a square root.

The factor group $\mathbb{R} / \mathbb{Z}$ under addition has an infinite number of elements of order 4

Is every finite simple group a quotient of a braid group?

Isomorphism between isomorphic abelian groups quotiented by isomorphic subgroups

Writing a quotient group as a product of cyclic groups

Meaning of factorization of groups

Element in a coset whose order's prime divisors are those of the order of the coset

What is meant by the phrase "but the identity in a quotient group is the subgroup" in this Abstract Algebra proof?

2-groups with abelianization of type (2,2)

Is it always $|G:gG|=1$ where $G$ is a group and $g \in G$?

Elements of $\mathbb{Z}_6 / \mathbb{Z}_2$

Quotient group with $\mathbb{Z}_2$ and $\mathbb{Z}_4$

Subgroups of self dual groups

Quotient of the group $\mathbb{Z}^2 \oplus \mathbb{Z} ^2 \oplus \mathbb{Z} ^2$

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