Abstract: | A Fitting class $ \mathfrak{F} A Fitting class is said to be π-maximal if is an inclusion maximal subclass of the Fitting class of all finite soluble π-groups. We prove that is a π-maximal Fitting class exactly when there is a prime p ∊ π such that the index of the -radical in G is equal to 1 or p for every π-subgroup of G. Hence, there exist maximal subclasses in a local Fitting class. This gives a negative answer to Skiba’s conjecture that
there are no maximal Fitting subclasses in a local Fitting class (see 1, Question 13.50]).
Original Russian Text Copyright ? 2008 Savelyeva N. V. and Vorob’ev N. T.
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Vitebsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 6, pp. 1411–1419, November–December, 2008. |