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Saturated closure of homomorphs. (English) Zbl 0832.20033
Let \(\pi\) be a set of primes and \(\pi'\) the complement to \(\pi\) in the set of all primes. A group \(G\) is said to be \(\pi\)-solvable if every chief factor of \(G\) is either a solvable \(\pi\)-group or a \(\pi'\)-group. The paper deals with a characterization of the saturated closure of a homomorph of finite \(\pi\)-solvable groups, by means of the semicovering subgroups.

MSC:
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D30 Series and lattices of subgroups
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20F17 Formations of groups, Fitting classes
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