List questions from group-isomorphism

Published on 19 Sep 2020 - 16:20

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Proving that $f^{-1} \in \operatorname{Hom}(Y,X).$

Published on 22 Sep 2020 - 22:56

263

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If $G$ is a group with, then the subgroup of $S_n$ constructed in the proof of Cayley’s theorem is a transitive subgroup of $S_G$

Published on 06 Apr 2026 - 9:29

63

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Identify the isomorphism of the group $D_6 / \langle\rho ^3\rangle$.

Published on 28 Mar 2026 - 21:06

204

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"Short exact sequence split" answer illustration.

Published on 31 Mar 2026 - 9:50

43

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Let, $N,K,N',K'$ be groups and $N\cong N',K\cong K'$. Does $N\rtimes K\cong N'\rtimes K'$?

Published on 30 Mar 2026 - 8:08

94

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Isomorphisms of $S_n$

Published on 06 Apr 2026 - 12:26

61

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$\mathbb{C}^{*}$ as a direct product of two subgroups. (Hint: polar form)

Published on 28 Mar 2026 - 1:24

90

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How to prove that these groups are isomorphic (or not)?

Published on 02 Oct 2020 - 16:08

159

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What is the connection between $(G/K)(H/K) \cong G/H$ and this commutative diagram? (Lang's Algebra, p. 17)

Published on 31 Mar 2026 - 7:57

97

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Prove or disprove if its isomorphic.

Published on 05 Oct 2020 - 15:25

137

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Proof that $(A/I)/(J/I)$ is isomorphic to $A/J$

Published on 05 Oct 2020 - 21:18

125

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Checking that the given function is really a homomorphism.

Published on 25 Mar 2026 - 16:06

1.2k

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find number of automorphisms of (Z,+)

Published on 06 Oct 2020 - 4:02

287

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Prove isomorphism of group

Published on 06 Oct 2020 - 5:05

List Question

Are two groups isomorphic if each is isomorphic to a subgroup of the other?

Proving that $f^{-1} \in \operatorname{Hom}(Y,X).$

If $G$ is a group with, then the subgroup of $S_n$ constructed in the proof of Cayley’s theorem is a transitive subgroup of $S_G$

Identify the isomorphism of the group $D_6 / \langle\rho ^3\rangle$.

"Short exact sequence split" answer illustration.

Let, $N,K,N',K'$ be groups and $N\cong N',K\cong K'$. Does $N\rtimes K\cong N'\rtimes K'$?

Isomorphisms of $S_n$

$\mathbb{C}^{*}$ as a direct product of two subgroups. (Hint: polar form)

How to prove that these groups are isomorphic (or not)?

What is the connection between $(G/K)(H/K) \cong G/H$ and this commutative diagram? (Lang's Algebra, p. 17)

Prove or disprove if its isomorphic.

Proof that $(A/I)/(J/I)$ is isomorphic to $A/J$

Checking that the given function is really a homomorphism.

find number of automorphisms of (Z,+)

Prove isomorphism of group

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