Let m be a positive integer and let Ω be a finite set. The m-closure of G≤Sym(Ω) is the largest permutation group on Ω having the same orbits as G in its induced action on the Cartesian product Ωm. The 1-closure and 2-closure of a solvable permutation group need not be solvable. We prove that the m-closure of a solvable permutation group is always solvable for m≥3.
Предметные области OECD FOS+WOS
- 1.01 МАТЕМАТИКА