Geodesic
On $\mathfrak{F}$-radicals of finite $\pi$-soluble groups
Algebra and discrete mathematics, no. 3 (2006), pp. 49-54

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In this paper, we prove that for every local $\pi$-saturated Fitting class $\mathcal{F}$ with $char(\mathcal{F})=\mathbb{P}$, the $\mathcal{F}$-radical of every finite $\pi$-soluble groups $G$ has the property: $C_G(G_\mathcal{F})\subseteq G_\mathcal{F}$. From this, some well known results are followed and some new results are obtained.
Keywords: Finite group; $\pi$-soluble group; $\mathcal{F}$-radical, Fitting class. 
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     author = {Wenbin Guo and Xi Liu and Baojun Li},
     title = {On $\mathfrak{F}$-radicals of finite $\pi$-soluble groups},
     journal = {Algebra and discrete mathematics},
     pages = {49--54},
     publisher = {mathdoc},
     number = {3},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2006_3_a4/}
}
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Wenbin Guo; Xi Liu; Baojun Li. On $\mathfrak{F}$-radicals of finite $\pi$-soluble groups. Algebra and discrete mathematics, no. 3 (2006), pp. 49-54. http://geodesic.mathdoc.fr/item/ADM_2006_3_a4/