Transactions of the American Mathematical Society

Author(s): Silvio Dolfi
Journal: Trans. Amer. Math. Soc. 360 (2008), 135-152.
MSC (2000): Primary 20D45; Secondary 20D20
Posted: August 20, 2007
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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

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.

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Silvio Dolfi
Affiliation: Dipartimento di Matematica ``U. Dini'', Università degli Studi di Firenze, Firenze, 50134 Italy
Email: dolfi@math.unifi.it

DOI: 10.1090/S0002-9947-07-04155-4
PII: S 0002-9947(07)04155-4
Keywords: Finite groups, coprime action, regular orbits.
Received by editor(s): May 7, 2004
Received by editor(s) in revised form: September 7, 2005
Posted: August 20, 2007
Additional Notes: This research was partially supported by MURST project `Teoria dei Gruppi e Applicazioni'.
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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