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Distribution of balls into boxes.

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#permutations #combinations #permutation-cycles
60
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How to proof (step-by-step) that

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#group-theory #symmetric-groups #permutation-cycles
57
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Let be $\sigma=(1\cdots n) \in S_n$. Then $C_{S_{n}}(\sigma) = \langle \sigma \rangle$.

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#group-theory #symmetric-groups #permutation-cycles
52
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In the Burnside book "Theory of Groups of Finite Order" -- error on page 3?

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#abstract-algebra #group-theory #permutations #finite-groups #permutation-cycles
658
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Choice of generator in dihedral group

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#group-theory #permutations #dihedral-groups #permutation-cycles
38
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How to find the number of left coset of $H$ in symmetric group $S_7$

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#group-theory #symmetric-groups #permutation-cycles
222
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How to prove there is no order $15$ permutation in $S_7$?

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#group-theory #permutation-cycles
38
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There exists a group element $\sigma\in S_7$ under some conditions?

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#group-theory #symmetric-groups #permutation-cycles
68
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Calculating a product of 3-cycles

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#abstract-algebra #group-theory #permutations #proof-explanation #permutation-cycles
329
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Prove that $Z(S_n)=\{1\}$ for all $n\geq 3$.

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#group-theory #symmetric-groups #group-actions #permutation-cycles
1.3k
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How many cycles in this adjacency matrix?

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#combinatorics #permutation-cycles #adjacency-matrix
45
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$\beta^k $ is a cycle ⟺ gcd($k$ , o($\beta$))=$1$

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#group-theory #permutations #permutation-cycles
110
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The number of inversions of an arithmetic progression modulo some number

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#permutations #computational-complexity #arithmetic-progressions #permutation-cycles
1.1k
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Determine all quotient group of $S_3$ and the corresponding homomorphism image.

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#group-theory #permutation-cycles
60
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All permutation groups acting on a finite set are closed

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#group-theory #permutations #solution-verification #permutation-cycles

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