List questions from group-isomorphism

Published on 30 Jun 2021 - 22:31

485

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Short five lemma and a counterexample: commutative diagram

Published on 25 Mar 2026 - 17:19

218

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Isomorphism between $D_3$ and $S_3$

Published on 29 Mar 2026 - 6:28

67

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Showing that $G/N \cong A \times (B / N)$

Published on 30 Mar 2026 - 15:00

215

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Are all bijections from a finite cyclic group to itself isomorphisms, if generators are mapped only to generators?

Published on 06 Apr 2026 - 8:04

115

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Does the number of involutions in an abelian group of order $2^n$ uniquely determine its isomorphism class?

Published on 09 Jul 2021 - 17:30

1.2k

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Show $U_t(st)$ isomorphic to $U(s)$

Published on 12 Jul 2021 - 20:42

90

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$H\leq K \leq G$ and $K \trianglelefteq G \Rightarrow$ $K/H \trianglelefteq G/H$.

Published on 18 Jul 2021 - 4:30

128

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U-groups and internal direct product

Published on 24 Jul 2021 - 4:16

445

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Possibilities of an automorphism on $Z_{20}$

Published on 01 Apr 2026 - 7:17

188

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Bijective proof involving fixed points and symmetric group on $n$ letters?

Published on 26 Jul 2021 - 11:56

287

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Is it true that $G\cong (G/H)\times H$ for every abelian group $G$ and every subgroup $H\le G\;?$

Published on 28 Jul 2021 - 20:41

54

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For which $m,n>1$ is $D_{mn} \cong D_n \times\Bbb Z/m\Bbb Z?$

Published on 28 Mar 2026 - 13:11

63

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Proof that $(\mathbb{Z}[x], +) \times \mathbb{Z} \times \mathbb{Z} \cong (\mathbb{Z}[x], +) \times \mathbb{Z}$

Published on 07 Apr 2026 - 21:30

201

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Central product isomorphism: $Z_4 * Q_8 \cong Z_4 * D_8$

Published on 28 Mar 2026 - 13:11

List Question

Prove $\mathbb{Z_m} \times \mathbb{Z}_n \cong \mathbb{Z}_d \times \mathbb{Z}_l$

Short five lemma and a counterexample: commutative diagram

Isomorphism between $D_3$ and $S_3$

Showing that $G/N \cong A \times (B / N)$

Are all bijections from a finite cyclic group to itself isomorphisms, if generators are mapped only to generators?

Does the number of involutions in an abelian group of order $2^n$ uniquely determine its isomorphism class?

Show $U_t(st)$ isomorphic to $U(s)$

$H\leq K \leq G$ and $K \trianglelefteq G \Rightarrow$ $K/H \trianglelefteq G/H$.

U-groups and internal direct product

Possibilities of an automorphism on $Z_{20}$

Bijective proof involving fixed points and symmetric group on $n$ letters?

Is it true that $G\cong (G/H)\times H$ for every abelian group $G$ and every subgroup $H\le G\;?$

For which $m,n>1$ is $D_{mn} \cong D_n \times\Bbb Z/m\Bbb Z?$

Proof that $(\mathbb{Z}[x], +) \times \mathbb{Z} \times \mathbb{Z} \cong (\mathbb{Z}[x], +) \times \mathbb{Z}$

Central product isomorphism: $Z_4 * Q_8 \cong Z_4 * D_8$

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