On the Shemetkov Problem for Fitting Classes ∗
نویسندگان
چکیده
Suppose that π be a set of primes and F a local Fitting class. Let Kπ(F) be the set of finite π-soluble groups with a Hall πsubgroup belonging to F. In this paper, we show that the class Kπ(F) is a local Fitting class. Thus, an interesting Shemetkov question for Fitting classes will be answered positively. By using the result, the F-radical of a Hall π-subgroup of a finite π-soluble group is described. For an H-function f , we also give the definition and its description of f -radical of a finite π-soluble group. Some known important results follow. MSC 2000: 20D10, 20D20, 20D25
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