Let G be a permutation group on a finite set Omega. If G does not involve A(n) for n greater than or equal to 5, then there exist two disjoint subsets of Ohm such that no Sylow subgroup of G stabilizes both and four disjoint subsets of Ohm whose stabilizers in G intersect trivially.
ORBITS OF A PERMUTATION GROUP ON THE POWER SET / S. DOLFI. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - STAMPA. - 75:(2000), pp. 321-327. [10.1007/s000130050510]
ORBITS OF A PERMUTATION GROUP ON THE POWER SET
DOLFI, SILVIO
2000
Abstract
Let G be a permutation group on a finite set Omega. If G does not involve A(n) for n greater than or equal to 5, then there exist two disjoint subsets of Ohm such that no Sylow subgroup of G stabilizes both and four disjoint subsets of Ohm whose stabilizers in G intersect trivially.
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