List questions from group-isomorphism

Published on 19 Apr 2020 - 17:42

495

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General Cayley's theorem: Let $G$ be a group and $H$ a subgroup of $G$ such that $[G:H]=n$.

Published on 29 Mar 2026 - 12:11

323

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How to show $G_{m}\cong G_n $ if and only if $n=m$, where $G_m:= \langle x,y \mid x(yx)^{m}=y(xy)^{m}\rangle$

Published on 25 Mar 2026 - 23:13

77

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Understand abelian group theorem

Published on 30 Mar 2026 - 20:36

70

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Prove $\text{Inn}(\mathbb{Q_8}) \cong \mathbb{Q_8}/ Z(\mathbb{Q_8})$

Published on 29 Mar 2026 - 13:41

92

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Prove that $\mathbb {D}_4 $ is isomorphic with $\mathbb {Z}_2 \times\mathbb{Z}_2 \times\mathbb{Z}_2$

Published on 26 Mar 2026 - 16:05

40

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Existence on an isomorphic permutation group

Published on 24 Apr 2020 - 16:18

317

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Prove that there is an isomorphism between two groups.

Published on 28 Mar 2026 - 11:15

123

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Is group extension unique?

Published on 25 Mar 2026 - 12:30

746

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One dimensional representation and Commutator subgroup

Published on 28 Apr 2020 - 7:21

350

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Proving / Disproving the group is isomorphic when it itself is built of isomorphisms

Published on 30 Apr 2020 - 19:28

22

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Subgroups of General Linear Group containing Special Linear Group, from 3rd isomorphism theorem

Published on 01 May 2020 - 22:03

50

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the isomorphism between two matrix groups

Published on 26 Mar 2026 - 12:51

771

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(Soft Question) What kinds of properties are transferred by isomorphisms?

Published on 02 May 2020 - 19:57

53

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determine whether the following are surjective homomorphisms and if so are they also isomorphisms by computing kernels

Published on 28 Mar 2026 - 11:22

List Question

"Cross-multiplying" isomorphic quotient groups?

General Cayley's theorem: Let $G$ be a group and $H$ a subgroup of $G$ such that $[G:H]=n$.

How to show $G_{m}\cong G_n $ if and only if $n=m$, where $G_m:= \langle x,y \mid x(yx)^{m}=y(xy)^{m}\rangle$

Understand abelian group theorem

Prove $\text{Inn}(\mathbb{Q_8}) \cong \mathbb{Q_8}/ Z(\mathbb{Q_8})$

Prove that $\mathbb {D}_4 $ is isomorphic with $\mathbb {Z}_2 \times\mathbb{Z}_2 \times\mathbb{Z}_2$

Existence on an isomorphic permutation group

Prove that there is an isomorphism between two groups.

Is group extension unique?

One dimensional representation and Commutator subgroup

Proving / Disproving the group is isomorphic when it itself is built of isomorphisms

Subgroups of General Linear Group containing Special Linear Group, from 3rd isomorphism theorem

the isomorphism between two matrix groups

(Soft Question) What kinds of properties are transferred by isomorphisms?

determine whether the following are surjective homomorphisms and if so are they also isomorphisms by computing kernels

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