Analyzes the structure of finite groups with p-quasinormality and details new characterizations of nilpotent and supersolvable groups.
For a nontrivial [Formula: see text]-group [Formula: see text], a maximal chain of [Formula: see text] is a chain of subgroups [Formula: see text] with [Formula: see text] for [Formula: see text], where [Formula: see text] is an integer. We determine the structure of finite groups having [Formula: see text]-quasinormality of a maximal chain of Sylow subgroups. We obtain new characterizations of finite [Formula: see text]-nilpotent groups and supersolvable groups.
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Yong Xu (2026) studied this question.
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