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15
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Combinatorial proof of the identity relating Hurwitz numbers

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#combinatorics #symmetric-groups #combinatorial-proofs #algebraic-combinatorics
162
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God's number for the 3x3x3 Picture Cube

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#combinatorics #group-theory #symmetric-groups #rubiks-cube
31
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Find normaliser of $S_{n-1}$ in $S_n$.

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#group-theory #proof-verification #symmetric-groups
612
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Application of the correspondence theorem for groups

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#group-theory #symmetric-groups #normal-subgroups #group-isomorphism
20
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Sequence of monotonic transposition characterisation

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#group-theory #permutations #symmetric-groups #permutation-cycles #symmetric-algebra
1k
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Calculator/Tool to find subgroup of $S_n$ generated by $\langle g_1 \dots g_k \rangle$

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#symmetric-groups
99
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What kind of group product is this?

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#abstract-algebra #group-theory #permutations #symmetric-groups #products
43
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Isomorphism composed with a certain conjugation fixes (some) 2-cycles in $S_n$

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#group-theory #symmetric-groups #group-isomorphism #automorphism-group
149
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How to find a p-Sylow for symmetric group $S_{p^2}$？

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#abstract-algebra #group-theory #symmetric-groups #sylow-theory #semidirect-product
54
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On $p$-Sylows for $S_{2p}$ ... $S_{(p-1)p}$

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#abstract-algebra #group-theory #symmetric-groups #sylow-theory
1.9k
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Show that ${\rm Aut}(Z_2 \times Z_2) \cong S_3$

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#abstract-algebra #group-theory #symmetric-groups #group-isomorphism #automorphism-group
37
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Define $\varphi:S_4\to S_4$ via $\alpha\mapsto(1 3 4)\alpha$. How would I prove $\varphi$ is not a homorphism?

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#group-theory #symmetric-groups #group-homomorphism
81
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Permutation with largest odd order

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#group-theory #number-theory #optimization #permutations #symmetric-groups
191
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Normal subgroups of signed symmetric groups

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#group-theory #permutations #symmetric-groups #normal-subgroups
121
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2D symmetry group with 1 or more rotations (nontrivial) but exactly 1 reflection (nontrivial)

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#group-theory #rotations #symmetric-groups #symmetry #reflection

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