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11.25 (1990)

Partially Solved

For the definition of the product of Fitting classes see (N. T. Vorob’ev, Math. Notes, 43, no. 2 (1988), 91–94).
$\qquad$ a) Does there exist a local product (different from the class of all finite groups and from the class of all finite soluble groups) of Fitting classes each of which is not local and is not a formation?
$\qquad$ b) Do there exist local Fitting classes which are decomposable into a non-trivial product of Fitting classes and in every such a decomposition all factors are non-local?

Contributor: N. T. Vorob’ëv

Progress

a) Yes, there does (N. T. Vorob’ev, A. N. Skiba, Problems in Algebra, 8, Gomel’, 1995, 55–58 (Russian)).

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