List questions from group-isomorphism

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Let $p<q$ be distinct prime numbers and $G$ be a group with $|G|=pq$

Published on 24 Mar 2016 - 19:03

439

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If an automorphism sends more than half of the elements to themselves then it's the identity

Published on 30 Mar 2026 - 12:00

35

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Computation of Factor Groups

Published on 26 Mar 2016 - 21:14

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How to check in GAP whether two groups are isomorphic

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Is $\mathbb{C}^{\times}/\mathbb{R}^{\times}$ isomorphic to $\mathbb{C}^{\times}/\{\pm 1\}$

Published on 28 Mar 2016 - 21:25

1.5k

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Eigenvalues and eigenspaces with isomorphisms

Published on 29 Mar 2016 - 18:50

591

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Isomorphism of Quotient Subgroups

Published on 02 Apr 2026 - 20:09

945

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Isomorphic and Homomorphic

Published on 01 Apr 2026 - 12:45

4.4k

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Steps to prove or disprove if two rings are isomorphic

Published on 02 Apr 2016 - 17:01

358

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$G=\langle a,b \mid abab^{-1}\rangle$ and $H=\langle c,d \mid c^2d^2\rangle$ are isomorphic (Can't use Seifert/van Kampen Theorem)

Published on 28 Mar 2026 - 2:07

1k

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Prove that additive order is preserved by isomorphisms

Published on 04 Apr 2016 - 14:37

3.3k

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Character of $Sym^2(V)$ and decomposition into irreducible representations

Published on 28 Mar 2026 - 9:50

1.4k

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$A_4$ is not isomorphic to $D_6$

Published on 05 Apr 2016 - 1:39

56

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Proving that a function is an isomorphism of groups

Published on 29 Mar 2026 - 15:59

List Question

If $G \to G'$ are isomorphic groups, then $|Aut(G)| = |$ all isomophisms $G \to G'|$.

Let $p<q$ be distinct prime numbers and $G$ be a group with $|G|=pq$

If an automorphism sends more than half of the elements to themselves then it's the identity

Computation of Factor Groups

How to check in GAP whether two groups are isomorphic

Is $\mathbb{C}^{\times}/\mathbb{R}^{\times}$ isomorphic to $\mathbb{C}^{\times}/\{\pm 1\}$

Eigenvalues and eigenspaces with isomorphisms

Isomorphism of Quotient Subgroups

Isomorphic and Homomorphic

Steps to prove or disprove if two rings are isomorphic

$G=\langle a,b \mid abab^{-1}\rangle$ and $H=\langle c,d \mid c^2d^2\rangle$ are isomorphic (Can't use Seifert/van Kampen Theorem)

Prove that additive order is preserved by isomorphisms

Character of $Sym^2(V)$ and decomposition into irreducible representations

$A_4$ is not isomorphic to $D_6$

Proving that a function is an isomorphism of groups

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