List questions from semidirect-product

Published on 22 Mar 2026 - 19:26

788

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Interpretation of wreath products in general and on symmetric groups

Published on 22 Mar 2026 - 11:32

64

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The commutator of two subgroup in a finite group

Published on 17 Mar 2026 - 10:55

1.7k

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Why is the symmetry group $S_3$ not the direct product of two nontrivial groups?

Published on 19 Mar 2026 - 20:18

312

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Holomorph of a group $G$, then the automorphism of $G$ are inner automorphisms

Published on 19 Mar 2026 - 12:47

786

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$U(n)=SU(n)\rtimes U(1)$?

Published on 20 Mar 2026 - 21:44

120

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Automorphism group of $\operatorname{Hol}(\mathbb{Z_n})$

Published on 19 Mar 2026 - 21:16

80

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Groups without using Sylow

Published on 20 Mar 2026 - 7:41

102

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Product of two elements in a semidirect product with distinct prime powers

Published on 20 Mar 2026 - 5:19

42

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Proving that there exist a semidirect group

Published on 19 Mar 2026 - 22:13

350

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Prove that for the semidirect product $\mathbb{Z}_5 \rtimes \mathbb{Z}_3$, the homomorphism $\alpha$ is trivial

Published on 19 Mar 2026 - 20:20

52

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Identify some Coxeter group

Published on 20 Mar 2026 - 22:33

95

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smallest splitting field and Galois expansion

Published on 25 Mar 2026 - 1:16

175

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How many non-abelian groups of order $lpq$ are there?

Published on 24 Mar 2026 - 23:46

77

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Prove $\hat{G}\rtimes Aut(G)$ is primitive when $G$ is characteristically simple

Published on 20 Mar 2026 - 8:25

List Question

Online reference about semi-direct products in finite group theory?

Interpretation of wreath products in general and on symmetric groups

The commutator of two subgroup in a finite group

Why is the symmetry group $S_3$ not the direct product of two nontrivial groups?

Holomorph of a group $G$, then the automorphism of $G$ are inner automorphisms

$U(n)=SU(n)\rtimes U(1)$?

Automorphism group of $\operatorname{Hol}(\mathbb{Z_n})$

Groups without using Sylow

Product of two elements in a semidirect product with distinct prime powers

Proving that there exist a semidirect group

Prove that for the semidirect product $\mathbb{Z}_5 \rtimes \mathbb{Z}_3$, the homomorphism $\alpha$ is trivial

Identify some Coxeter group

smallest splitting field and Galois expansion

How many non-abelian groups of order $lpq$ are there?

Prove $\hat{G}\rtimes Aut(G)$ is primitive when $G$ is characteristically simple

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