Let G be a p-soluble group. Then G has a subnormal series whose factors are either p′-groups or Abelian p-groups. The smallest number of Abelian p-factors in all subnormal series of G of this kind is called the derived p-length of G. A subgroup H of the group G is called a Fitting subgroup if H ≤ F(G). The existence of a functional dependence of the estimate of derived p-length of a p-soluble group on the value of indices of the Fitting p-subgroups in their normal closures is established.

中文翻译：

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p-可溶性基团的p-长度，在正常闭包中具有拟合p-子群的有界指标

令G为p-可溶基团。然后，G具有一个次正规序列，其因子为p'- groups或Abelian p -groups。阿贝尔的最小数目p在所有低于正常系列-因子ģ这种被称为导出p的-length G.一个分组ħ组ģ被称为Fitting子群如果ħ ≤ ˚F（ģ）。衍生的估计的函数依赖关系的存在p a的-length p在拟合的p-子组的正常封闭指数的值上建立了可溶基团。