The Classification of Permutation Groups with Maximum Orbits
DOI:
https://doi.org/10.24297/jam.v15i0.7926Keywords:
permutation group, bounded movement, orbits, permutation group, bounded movement, orbitsAbstract
Let G be a permutation group on a set with no fixed points in and let m be a positive integer. If no element of G moves any subset of by more than m points (that is, if 
for every and g 2 G), and the lengths two of orbits is p, and the restof orbits have lengths equal to 3. Then the number t of G-orbits in is at most 
Moreover, we classifiy all groups for
is hold.(For 
denotes the greatest integer less than or equal to x.)
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