Geodesic
Local factorisations of nonlocal Fitting classes
Diskretnaya Matematika, Tome 20 (2008) no. 3, pp. 111-118
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We consider general rules of constructing of local products of the Fitting classes with the use of nonlocal factors determined by the minimal elements of the Lockett section. We give a simple method to construct local Fitting classes which are factorised by nonlocal Fitting classes of some classes of $\pi$-groups and $\pi'$-groups. Applying the class $\mathfrak B$, we simplify the procedure of construction of a nonlocal factor in the local product. It is shown that in the construction of the local product the nonlocal factor for the appropriate set of primes $\pi$ is the Fitting class of the form $\mathfrak B_*\mathfrak S_\pi$, where $\mathfrak B_*$ is the minimal element of the Lockett section of the class $\mathfrak B$. In this paper, we consider only finite solvable groups. 
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V. V. Shpakov; N. T. Vorob'ev. Local factorisations of nonlocal Fitting classes. Diskretnaya Matematika, Tome 20 (2008) no. 3, pp. 111-118. http://geodesic.mathdoc.fr/item/DM_2008_20_3_a10/

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