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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 3, pp. 366–370, March, 2020.
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Gritsuk, D.V., Trofimuk, A.A. Derived p-Length of a p-Soluble Group with Bounded Indices of Fitting p-Subgroups in Their Normal Closures. Ukr Math J 72, 416–421 (2020). https://doi.org/10.1007/s11253-020-01791-0
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DOI: https://doi.org/10.1007/s11253-020-01791-0