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- W2964314114 abstract "Let $G$ be a finite solvable group and $H$ be a subgroup of $Aut(G)$. Suppose that there exists an $H$-invariant Carter subgroup $F$ of $G$ such that the semidirect product $FH$ is a Frobenius group with kernel $F$. We prove that the terms of the Fitting series of $C_{G}(H)$ are obtained as the intersection of $C_{G}(H)$ with the corresponding terms of the Fitting series of $G$, and the Fitting height of $G$ may exceed the Fitting height of $C_{G}(H)$ by at most one. As a corollary it is shown that for any set of primes $pi$, the terms of the $pi$-series of $C_{G}(H)$ is obtained as the intersection of $C_{G}(H)$ with the corresponding terms of the $pi$-series of $G$, and the $pi$-length of $G$ may exceed the $pi$-length of $C_{G}(H)$ by at most one. They generalize the main results of cite{Khu}." @default.
- W2964314114 created "2019-07-30" @default.
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- W2964314114 date "2019-07-25" @default.
- W2964314114 modified "2023-09-27" @default.
- W2964314114 title "Frobenius action on Carter subgroups" @default.
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