List questions from quotient-group

Published on 17 Mar 2026 - 21:22

38

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Comparing centers of group and a subgroup

Published on 24 Mar 2026 - 19:28

67

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Intuitive understanding of $g^iH=(gH)^i$ factor groups

Published on 20 Mar 2026 - 3:50

72

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Is it true that $(\mathbb{Z}\bigoplus\mathbb{Z}\bigoplus\mathbb{Z})/(\mathbb{Z}\bigoplus\mathbb{Z})\cong\mathbb{Z}$

Published on 20 Mar 2026 - 13:30

98

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Quotient rings as complements of ideals

Published on 20 Mar 2026 - 8:46

89

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If a proper subgroup of maximal order is solvable and normal, then the group is solvable. Generalization.

Published on 22 Mar 2026 - 6:19

67

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Do the results hold for isomorphisms of groups?

Published on 22 Mar 2026 - 11:51

112

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tesselations in $1$ dimension (i.e., tiling a quotient group of integers with same-shaped subsets)

Published on 24 Mar 2026 - 12:38

141

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Cardinality of a quotient

Published on 22 Mar 2026 - 7:58

87

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Centralizers of non-central elements of a special group

Published on 20 Mar 2026 - 19:11

323

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Is $P/Z(P)$ cyclic when $Z(P)$ is not trivial?

Published on 20 Mar 2026 - 6:11

1.6k

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Why in Quotient Group we need normal subgroup?

Published on 23 Mar 2026 - 9:30

38

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Representatives of normal subgroups and intersections

Published on 23 Mar 2026 - 11:53

1k

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Let $H$ be the Heisenberg group. Determine the center $Z(H)$ of $H$. Show that the quotient group $H/Z(H)$ is abelian.

Published on 23 Mar 2026 - 16:04

315

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Any large group is SQ-universal.

Published on 23 Mar 2026 - 15:32

List Question

Show $\varphi:R/I\to R/J$ is a well-defined ring homomorphism

Comparing centers of group and a subgroup

Intuitive understanding of $g^iH=(gH)^i$ factor groups

Is it true that $(\mathbb{Z}\bigoplus\mathbb{Z}\bigoplus\mathbb{Z})/(\mathbb{Z}\bigoplus\mathbb{Z})\cong\mathbb{Z}$

Quotient rings as complements of ideals

If a proper subgroup of maximal order is solvable and normal, then the group is solvable. Generalization.

Do the results hold for isomorphisms of groups?

tesselations in $1$ dimension (i.e., tiling a quotient group of integers with same-shaped subsets)

Cardinality of a quotient

Centralizers of non-central elements of a special group

Is $P/Z(P)$ cyclic when $Z(P)$ is not trivial?

Why in Quotient Group we need normal subgroup?

Representatives of normal subgroups and intersections

Let $H$ be the Heisenberg group. Determine the center $Z(H)$ of $H$. Show that the quotient group $H/Z(H)$ is abelian.

Any large group is SQ-universal.

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