List questions from group-isomorphism

Published on 09 Apr 2026 - 20:54

72

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Is $f(x)=k \log x$ the only solution to the equation $\sum_{i=1}^{n}f(x_{i})=f(\prod_{i=1}^{n}x_{i})$?

Published on 15 Apr 2026 - 20:28

266

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Finding an isomorphic subring of matrices

Published on 10 May 2026 - 21:52

335

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What is an outer automorphism?

Published on 09 Apr 2026 - 21:14

98

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In a cyclic group with subgroup $H$ and $N$, list the elements in $H + N$ and $H \cap N$

Published on 17 Apr 2026 - 13:20

52

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Find all the natural numbers such that $Z_n$ is isomorphic to the dihedral group $D_n$

Published on 16 Apr 2026 - 0:27

1.2k

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What is a local group isomorphism?

Published on 09 Apr 2026 - 5:01

107

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Non-trivial isomorphism between the dihedral group to itself.

Published on 10 May 2026 - 16:33

48

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Prove that $G_2=\{B_1,B_2,...,B_p\}$ is a multiplicative group isomorphic with $G_1=\{A_1,A_2,...,A_p\}$

Published on 15 Apr 2026 - 16:30

196

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Group-subsets of monoids with different identities

Published on 10 May 2026 - 21:27

42

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Left representation is isomorphic to group

Published on 16 Apr 2026 - 18:34

97

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Let $H=\{\alpha \in S_7 :\alpha(3)=3\}$ and $K=\{\alpha \in S_7:\alpha(5)=5\}$. Prove that $H\cong K$.

Published on 12 Apr 2026 - 1:04

534

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Let $G,H$ be groups and $\varphi:G \times H\to G$ and $H'=\ker(\varphi)$. Show that $(G\times H)/H'\cong G$

Published on 14 May 2026 - 15:07

62

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Give three non-isomorphic groups of order 24, and explain why they are not isomorphic.

Published on 16 Apr 2026 - 8:51

480

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Index of a subgroup is preserved under group isomorphism

Published on 12 Apr 2026 - 7:52

List Question

Group Isomorphic problem

Is $f(x)=k \log x$ the only solution to the equation $\sum_{i=1}^{n}f(x_{i})=f(\prod_{i=1}^{n}x_{i})$?

Finding an isomorphic subring of matrices

What is an outer automorphism?

In a cyclic group with subgroup $H$ and $N$, list the elements in $H + N$ and $H \cap N$

Find all the natural numbers such that $Z_n$ is isomorphic to the dihedral group $D_n$

What is a local group isomorphism?

Non-trivial isomorphism between the dihedral group to itself.

Prove that $G_2=\{B_1,B_2,...,B_p\}$ is a multiplicative group isomorphic with $G_1=\{A_1,A_2,...,A_p\}$

Group-subsets of monoids with different identities

Left representation is isomorphic to group

Let $H=\{\alpha \in S_7 :\alpha(3)=3\}$ and $K=\{\alpha \in S_7:\alpha(5)=5\}$. Prove that $H\cong K$.

Let $G,H$ be groups and $\varphi:G \times H\to G$ and $H'=\ker(\varphi)$. Show that $(G\times H)/H'\cong G$

Give three non-isomorphic groups of order 24, and explain why they are not isomorphic.

Index of a subgroup is preserved under group isomorphism

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