Finite groups meet the criteria for a certain formation if their Sylow normalizers fit specified conditions, suggesting a classification approach.
Let N⊆ F⊆ D , let F be a saturated subgroup-closed formation, and let N and D be the formations of all nilpotent and all Ore dispersive finite groups, respectively. Sufficient conditions are obtained for a finite group to belong to F under the condition that the normalizers of all Sylow subgroups are contained in F .
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V. S. Monakhov (2025) studied this question.
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