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Large orbits in coprime actions of solvable groups


Author: Silvio Dolfi
Journal: Trans. Amer. Math. Soc. 360 (2008), 135-152
MSC (2000): Primary 20D45; Secondary 20D20
DOI: https://doi.org/10.1090/S0002-9947-07-04155-4
Published electronically: August 20, 2007
MathSciNet review: 2341997
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Abstract: Let $ G$ be a solvable group of automorphisms of a finite group $ K$. If $ \vert G\vert$ and $ \vert K\vert$ are coprime, then there exists an orbit of $ G$ on $ K$ 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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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9947-07-04155-4
Keywords: Finite groups, coprime action, regular orbits.
Received by editor(s): May 7, 2004
Received by editor(s) in revised form: September 7, 2005
Published electronically: August 20, 2007
Additional Notes: This research was partially supported by MURST project ‘Teoria dei Gruppi e Applicazioni’.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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