Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 48, No. 1, pp. 281289 (2007) 

On the Shemetkov problem for Fitting classesWenbin Guo and Baojun LiDepartment of Mathematics, Xuzhou Normal University, Xuzhou,221116, P.R.China, email: wbguo@xznu.edu.cn; Department of Mathematics, University of Science and Technology of China, Hefei 230026, P.R. ChinaAbstract: Suppose that $\pi$ be a set of primes and ${\frak F}$ a local Fitting class. Let $K_{\pi}({\frak F})$ be the set of finite $\pi$soluble groups with a Hall $\pi$subgroup belonging to ${\frak F}$. In this paper, we show that the class $K_{\pi}({\frak F})$ is a local Fitting class. Thus, an interesting Shemetkov question for Fitting classes will be answered positively. By using the result, the ${\frak F}$radical of a Hall $\pi$subgroup of a finite $\pi$soluble group is described. For a $H$function $f$, we also give the definition and its description of $f$radical of a finite $\pi$soluble group. Some known important results follow. Keywords: Fitting class; local Fitting class; Hall $\pi$subgroup; ${\frak F}$radical Classification (MSC2000): 20D10, 20D20, 20D25 Full text of the article:
Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.
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