List questions from symmetric-groups

Published on 05 Oct 2016 - 14:33

532

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Hint request: Find all elements of the group of symmetries of the octagon which commute with all other members of the group.

Published on 05 Oct 2016 - 21:44

390

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Show that the group of bijectives functions is not commutative

Published on 06 Oct 2016 - 3:28

606

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Find all the Sylow $2$ and the Sylow $3$ subgroups of $A_5$.

Published on 07 Oct 2016 - 7:41

232

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Consider the group $s_3$ of example 8.7

Published on 12 Oct 2016 - 10:03

62

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Show Composition Map $S_3 \to S_4/V$ is an isomorphism.

Published on 29 Mar 2026 - 7:33

99

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Formula for conjugating a permutation

Published on 15 Oct 2016 - 18:41

71

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Determining the subgroup $\langle V \cup \{(1,2,3)\}\rangle$

Published on 16 Oct 2016 - 11:42

548

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Centralizer in Symmetric Group of 7 elements.

Published on 16 Oct 2016 - 17:22

162

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Show that $S_n$ can be generated from the two-cycles $(1\,2),(1\,3),\dotsc,(1\,n)$.

Published on 16 Oct 2016 - 21:42

347

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Characters of semidirect and wreath products of non-Abelian finite groups

Published on 25 Mar 2026 - 6:12

702

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Show that a transposition cannot be written as a product of 3-cycles.

Published on 22 Oct 2016 - 0:26

77

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Using induction on n that if n is odd, then an n-cycle can be written as a product of 3-cycles.

Published on 22 Oct 2016 - 5:51

220

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Is this a special semidirect product?

Published on 26 Mar 2026 - 17:36

47

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Approaching Symmetric Groups-questions

Published on 23 Oct 2016 - 15:37

List Question

Cycle decomposition for elements of order 2 in $S_4$

Hint request: Find all elements of the group of symmetries of the octagon which commute with all other members of the group.

Show that the group of bijectives functions is not commutative

Find all the Sylow $2$ and the Sylow $3$ subgroups of $A_5$.

Consider the group $s_3$ of example 8.7

Show Composition Map $S_3 \to S_4/V$ is an isomorphism.

Formula for conjugating a permutation

Determining the subgroup $\langle V \cup \{(1,2,3)\}\rangle$

Centralizer in Symmetric Group of 7 elements.

Show that $S_n$ can be generated from the two-cycles $(1\,2),(1\,3),\dotsc,(1\,n)$.

Characters of semidirect and wreath products of non-Abelian finite groups

Show that a transposition cannot be written as a product of 3-cycles.

Using induction on n that if n is odd, then an n-cycle can be written as a product of 3-cycles.

Is this a special semidirect product?

Approaching Symmetric Groups-questions

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