List questions from symmetric-groups

Published on 11 Oct 2020 - 10:56

706

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Let $\sigma \in S_n$ be a product of $r$ disjoint cycles. Show that $\sigma$ can be written as $n-r$ transpositions.

Published on 11 Oct 2020 - 12:34

48

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Which of partitions of 5 correspond exclusively to even permutations?

Published on 26 Mar 2026 - 20:44

98

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Normalizer of any subset of $S_n$

Published on 12 Oct 2020 - 15:58

175

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Finding the orbit of an element in $S_5$

Published on 12 Oct 2020 - 17:48

62

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Number of homomorphisms from $G = \langle x,y\mid x^{-1}yx=y^6\rangle$ to $S_5$

Published on 27 Mar 2026 - 4:03

69

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Understanding why the hint will prove that $A_{5}$ is generated by $3$-cycles.

Published on 27 Mar 2026 - 7:20

90

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Checking if this proof of $A_{5}$ is generated by $3$-cycles is a complete proof?

Published on 27 Mar 2026 - 7:20

98

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Find a normalizer of order 3 in $S_7$ of cyclic subgroup in $S_7$

Published on 05 Apr 2026 - 13:49

225

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Show that $H$ of part $(c)$ contains all $3-$cycles.

Published on 15 Oct 2020 - 1:23

75

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Split $V \otimes V$ into simple $S_2$-representation.

Published on 16 Oct 2020 - 0:19

231

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Dummit Foote Exercise 1.7.10.a permutations of subsets self-study

Published on 18 Oct 2020 - 22:14

87

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Group of order $n!$

Published on 19 Oct 2020 - 0:26

228

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Prove that for any positive integer $n$, group $S'_n$＝$A_n$

Published on 19 Oct 2020 - 22:42

71

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Prove or disprove that $D_3 \times\mathbb Z_4$ has no subgroup of order 6.

Published on 20 Oct 2020 - 0:56

List Question

How many elements of order $5$ are there in $S_{12}$?

Let $\sigma \in S_n$ be a product of $r$ disjoint cycles. Show that $\sigma$ can be written as $n-r$ transpositions.

Which of partitions of 5 correspond exclusively to even permutations?

Normalizer of any subset of $S_n$

Finding the orbit of an element in $S_5$

Number of homomorphisms from $G = \langle x,y\mid x^{-1}yx=y^6\rangle$ to $S_5$

Understanding why the hint will prove that $A_{5}$ is generated by $3$-cycles.

Checking if this proof of $A_{5}$ is generated by $3$-cycles is a complete proof?

Find a normalizer of order 3 in $S_7$ of cyclic subgroup in $S_7$

Show that $H$ of part $(c)$ contains all $3-$cycles.

Split $V \otimes V$ into simple $S_2$-representation.

Dummit Foote Exercise 1.7.10.a permutations of subsets self-study

Group of order $n!$

Prove that for any positive integer $n$, group $S'_n$＝$A_n$

Prove or disprove that $D_3 \times\mathbb Z_4$ has no subgroup of order 6.

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