Let $G$ be a solvable group of automorphisms of a finite group $K$. If $\abs{G}$ and $\abs{K}$ are coprime, then there exists an orbit of $G$ on $K$ of size at least $\sqrt{\abs{G}}$. 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.
Large orbits in coprime actions of solvable groups / S. DOLFI. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 360, n.1:(2008), pp. 135-152.
Large orbits in coprime actions of solvable groups.
DOLFI, SILVIO
2008
Abstract
Let $G$ be a solvable group of automorphisms of a finite group $K$. If $\abs{G}$ and $\abs{K}$ are coprime, then there exists an orbit of $G$ on $K$ of size at least $\sqrt{\abs{G}}$. 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.File in questo prodotto:
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