List questions from automorphism-group

Published on 07 Apr 2022 - 14:38

70

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Is $\ker\varphi^2=(\ker\varphi)(\mathop{\rm im}\varphi\cap\ker\varphi^2)$ always true for group endomorphism $\varphi$?

Published on 12 Apr 2022 - 6:07

132

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Proving there exists a category corresponding to a group (Clara Loeh pg-14)

Published on 29 Mar 2026 - 17:25

71

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Show $\mathrm{Aut}(G)$ is a group: Question on proving closure

Published on 16 Apr 2022 - 1:42

109

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Intuition for finding a group $G$ such that $G \cong \mathrm{Aut}(G)$

Published on 17 Apr 2022 - 7:04

71

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Let $G$ be a non abelian simple group. Show that ${\rm Aut}(G^n)$ is isomorphic to ${\rm Aut}(G) \wr{\rm Sym}(n).$

Published on 25 Mar 2026 - 14:36

86

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Finite abelian group and its automorphism

Published on 18 Apr 2022 - 9:41

43

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Proof checking - Galois theory

Published on 21 Apr 2022 - 19:54

30

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Automorphism and cyclicity

Published on 25 Apr 2022 - 20:52

112

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Order of automorphisms of non-abelian group

Published on 25 Apr 2022 - 21:11

433

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Difference between bijection, homeomorphism and autohomeomorphism?

Published on 26 Apr 2022 - 9:20

79

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$p,q$ primes, $p\mid q-1$. Weaker assumption in the proof of the existence of non-trivial $C_p\ltimes C_q$?

Published on 01 Apr 2026 - 12:08

100

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How do we find the homorphism from $\mathbb{Z_2} \to{\rm Aut}(\mathbb{Z_3} \times \mathbb{Z_3})$

Published on 01 Apr 2026 - 12:07

374

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Classification of groups of order $18$

Published on 01 Apr 2026 - 12:06

153

Views

How to find the automorphism of $\mathbb{Z_3} \times \mathbb{Z}_5$

Published on 30 Apr 2022 - 2:55

List Question

olympiad problem using the fact that $|G|\leq f(|\mathrm{Aut}(G)|)$

Is $\ker\varphi^2=(\ker\varphi)(\mathop{\rm im}\varphi\cap\ker\varphi^2)$ always true for group endomorphism $\varphi$?

Proving there exists a category corresponding to a group (Clara Loeh pg-14)

Show $\mathrm{Aut}(G)$ is a group: Question on proving closure

Intuition for finding a group $G$ such that $G \cong \mathrm{Aut}(G)$

Let $G$ be a non abelian simple group. Show that ${\rm Aut}(G^n)$ is isomorphic to ${\rm Aut}(G) \wr{\rm Sym}(n).$

Finite abelian group and its automorphism

Proof checking - Galois theory

Automorphism and cyclicity

Order of automorphisms of non-abelian group

Difference between bijection, homeomorphism and autohomeomorphism?

$p,q$ primes, $p\mid q-1$. Weaker assumption in the proof of the existence of non-trivial $C_p\ltimes C_q$?

How do we find the homorphism from $\mathbb{Z_2} \to{\rm Aut}(\mathbb{Z_3} \times \mathbb{Z_3})$

Classification of groups of order $18$

How to find the automorphism of $\mathbb{Z_3} \times \mathbb{Z}_5$

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