List questions from abstract-algebra

Published on 13 Apr 2026 - 2:01

130

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$N$ and $M$ are normal subgroups, whose sizes are coprime. Show $|MN|=|M||N|$

Published on 10 May 2026 - 17:37

146

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Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$

Published on 10 May 2026 - 13:27

174

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Finding all subgroups of $\mathbb{Z}^2$ using algebraic topology.

Published on 10 May 2026 - 15:37

1.7k

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Sheaf Theory for Complex Analysis

Published on 10 May 2026 - 18:41

213

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Constructing the Monster

Published on 12 Apr 2026 - 2:20

355

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Universal Finitely Presented Group

Published on 10 May 2026 - 14:46

104

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the extension $E=\mathbb{Q}(\zeta)$ is an algebraic extension of $\mathbb{Q}$ of degree $ \ p-1 \ $

Published on 15 Apr 2026 - 2:43

148

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$\theta: R[x] \rightarrow R,$ $\ker(\theta) = (x)$ and it's a principal ideal?

Published on 11 May 2026 - 5:46

173

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Some nice basis for a subgroup of $Z^k$

Published on 11 May 2026 - 7:49

58

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higher K-theory: suspensions vs Clifford module bundles

Published on 13 May 2026 - 18:03

2.4k

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Is $G$ isomorphic to $\frac{G}{H}\times H$?

Published on 10 May 2026 - 16:06

307

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If $G\times K\cong H\times K$, is $G\cong H$?

Published on 14 May 2026 - 11:40

1.7k

Views

Exact sequence of $Hom(, M)$.

Published on 14 May 2026 - 8:59

474

Views

Example of Group that is not Internal direct product under weaker condition

Published on 10 May 2026 - 14:56

List Question

The group $\mathbb{Z}^n/A\mathbb{Z}^n$ is finite iff the determinant of A is nonzero

$N$ and $M$ are normal subgroups, whose sizes are coprime. Show $|MN|=|M||N|$

Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$

Finding all subgroups of $\mathbb{Z}^2$ using algebraic topology.

Sheaf Theory for Complex Analysis

Constructing the Monster

Universal Finitely Presented Group

the extension $E=\mathbb{Q}(\zeta)$ is an algebraic extension of $\mathbb{Q}$ of degree $ \ p-1 \ $

$\theta: R[x] \rightarrow R,$ $\ker(\theta) = (x)$ and it's a principal ideal?

Some nice basis for a subgroup of $Z^k$

higher K-theory: suspensions vs Clifford module bundles

Is $G$ isomorphic to $\frac{G}{H}\times H$?

If $G\times K\cong H\times K$, is $G\cong H$?

Exact sequence of $Hom(, M)$.

Example of Group that is not Internal direct product under weaker condition

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