Large orbits in coprime actions of solvable groups

By S. Dolfi. 2008

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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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ec984a52010e0dd453e208e5c05bb1fe37bbe140