List questions from symmetric-groups

Published on 27 Mar 2026 - 19:53

67

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Uniqueness of an order $3$ subgroup of $S_6$

Published on 12 Jan 2020 - 21:22

134

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Injective homomorphisms between group presentations

Published on 26 Mar 2026 - 4:49

120

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What is the cardinality of the set of all subgroups of $S_\alpha$ for infinite $\alpha$?

Published on 25 Mar 2026 - 23:42

52

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What is the asymptotic of the number of subgroups of $S_n$?

Published on 14 Jan 2020 - 18:30

220

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Induction step is not clear in Bóna's proof that the generating function of the alternating runs has $-1$ as a root of a certain multiplicity

Published on 14 Jan 2020 - 22:01

106

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Combinatorial bijection of primitive factorization

Published on 25 Mar 2026 - 10:59

83

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Can the normaliser of a p-Sylow-subgroup of S$_5$ be of odd cardinality?

Published on 27 Mar 2026 - 19:54

169

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Find a presentation with generators $g = (1,2)$ and $h = (2, 3)$ and three relations.

Published on 25 Mar 2026 - 20:18

184

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Can we define a natural isomorphism $\phi: S_4 \to {\rm Aut}(A_4)$?

Published on 19 Jan 2020 - 23:25

176

Views

Calculate all possible combinations of symmetries on a 10x10 square grid

Published on 26 Mar 2026 - 21:27

937

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Every finite simple group of order $n \geq 3$ is isomorphic to a subgroup of $A_n$

Published on 26 Mar 2026 - 2:57

71

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Compute $\sigma$, given $\sigma^{11}$ in $S_{10}.$

Published on 21 Jan 2020 - 13:16

159

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Number of homomorphisms $ \phi: _4 \to _4 $

Published on 26 Mar 2026 - 14:21

575

Views

Orders of the elements in the alternating group $A_n$

Published on 25 Jan 2020 - 11:23

List Question

Distinct $3$-Sylow subgroups of $S_6$ intersect trivially

Uniqueness of an order $3$ subgroup of $S_6$

Injective homomorphisms between group presentations

What is the cardinality of the set of all subgroups of $S_\alpha$ for infinite $\alpha$?

What is the asymptotic of the number of subgroups of $S_n$?

Induction step is not clear in Bóna's proof that the generating function of the alternating runs has $-1$ as a root of a certain multiplicity

Combinatorial bijection of primitive factorization

Can the normaliser of a p-Sylow-subgroup of S$_5$ be of odd cardinality?

Find a presentation with generators $g = (1,2)$ and $h = (2, 3)$ and three relations.

Can we define a natural isomorphism $\phi: S_4 \to {\rm Aut}(A_4)$?

Calculate all possible combinations of symmetries on a 10x10 square grid

Every finite simple group of order $n \geq 3$ is isomorphic to a subgroup of $A_n$

Compute $\sigma$, given $\sigma^{11}$ in $S_{10}.$

Number of homomorphisms $ \phi: _4 \to _4 $

Orders of the elements in the alternating group $A_n$

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