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Large orbits in coprime actions of solvable groups

Authors:	Silvio Dolfi

Institution:	Dipartimento di Matematica ``U. Dini', Università degli Studi di Firenze, Firenze, 50134 Italy

Abstract:	Let be a solvable group of automorphisms of a finite group . If $\vert G\vert$ and $\vert K\vert$ are coprime, then there exists an orbit of on of size at least $\sqrt{\vert G\vert}$ . It is also proved that in a $\pi$ -solvable group, the largest normal $\pi$ -subgroup is the intersection of at most three Hall $\pi$ -subgroups.

Keywords:	Finite groups coprime action regular orbits

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