Theoretical analysis establishes local criteria for p-supersolvability in finite p-solvable groups using restricted subfamilies of Pi-normal subgroups, suggesting simpler group structure...
Key Points
To establish local criteria for the p-supersolvability, supersolvability, and p-nilpotency of finite p-solvable groups using a restricted subfamily of maximal subgroups.
Analyzed embedding properties of a prescribed subfamily of maximal subgroups within a Sylow p-subgroup.
Evaluated condition constraints involving Π-normality in the Sylow normalizer and intermediate subgroups positioned between the derived subgroup and Frattini subgroup.
Demonstrated that a p-solvable group is p-supersolvable when a designated subfamily of Sylow maximal subgroups and an intermediate subgroup are Π-normal in the Sylow normalizer.
Generalized and relaxed prior embedding assumptions to yield unified criteria for both p-nilpotency and general supersolvability using minimal local subgroup data.