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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