On \(c\)-normal maximal and minimal subgroups of Sylow \(p\)-subgroups of finite groups. (English) Zbl 1050.20010

A subgroup \(H\) of a finite group \(G\) is said to be \(c\)-normal in \(G\) if there exists a subgroup \(N\) of \(G\) such that \(G=HN\) and \(H\cap N\) is contained in \(\text{Core}_G(H)\), the largest normal subgroup of \(G\) contained in \(H\). For a prime \(p\), the authors study the influence of the \(c\)-normality of the maximal subgroups of the Sylow \(p\)-subgroups of a group and the \(c\)-normality of some minimal subgroups on the structure of a group. They find some criteria for a finite group \(G\) to be \(p\)-nilpotent, \(p\)-supersoluble, or to belong to a saturated formation.


20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D40 Products of subgroups of abstract finite groups
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