Large orbits in coprime actions of solvable groups

Silvio Dolfi
2008 Transactions of the American Mathematical Society  
Let G be a solvable group of automorphisms of a finite group K. If |G| and |K| are coprime, then there exists an orbit of G on K of size at least |G|. It is also proved that in a π-solvable group, the largest normal π-subgroup is the intersection of at most three Hall π-subgroups.
doi:10.1090/s0002-9947-07-04155-4 fatcat:aslgeuyod5dl5p32qo7qcrakka