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math.GR2026
Commutators of signed -cycles
Philipp Bader, Bernhard Böhmler, Patrick Wegener
We show that for each element of the commutator subgroup in the symmetric group resp. in the signed symmetric group $(\mathbb{Z}/2\mathbb{Z})^n\rtimes\m…
math.GR2025
Commutators of n-cycles in the symmetric group
Philipp Bader
We show that for every even permutation on symbols is the commutator of two -cycles. More precisely, let be the symmetric group and the alternating gro…