What question did this study set out to answer?

The aim is to explore the structure of finite groups exhibiting p-quasinormality related to Sylow subgroups.

May 14, 2026

SS-Quasinormal Subgroups and p-Nilpotency of Finite Groups

Key Points

The aim is to explore the structure of finite groups exhibiting p-quasinormality related to Sylow subgroups.
Determined the structure of nontrivial p-groups regarding maximal chains of subgroups.
Analyzed characteristics associated with p-nilpotency and supersolvability of finite groups.
Established new characterizations for finite p-nilpotent groups.
Outlined distinct properties of supersolvable groups.

Abstract

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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