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Count the number of permutations of certain cycles type

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Confusing the order of two product of permutations

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271
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the order of a product two elements in symmetric group.

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14
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Number of times we have to compose a permutation in order to have exactly k fixed points

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39
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permutations cycle

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Number of permutations with cycle shape (2,2) in S5

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193
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Question in discrete mathematics about group permutations

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563
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Circular permutation with constraints

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150
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Propertie of the shift permutation

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65
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With $G=S_{5}$ acting on $X$ by conjugation, prove $|X|=10$.

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237
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Number of elements in the symmetric group with a particular transposition decomposition

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71
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Permutation group of objects which are themselves permutations

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76
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Make a 3-cycle with conjugation

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1.7k
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In S4, what is the subgroup generated by the cycle (123)?

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396
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Show than $(1,k+1), (1,2,3,...,n)$ generate the group $S_n$ if and only if $k$ and $n$ are coprime

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