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The influence of s-c-permutably embedded subgroups on the structure of finite groups. (English) Zbl 1228.20014
Summary: A subgroup \(H\) of a group \(G\) is said to be s-c-permutably embedded in \(G\) if every Sylow subgroup of \(H\) is a Sylow subgroup of some s-conditionally permutable subgroup of \(G\). In this paper, some new characterizations for a finite group to be \(p\)-supersoluble or \(p\)-nilpotent are obtained under the assumption that some of its maximal subgroups or 2-maximal subgroups of Sylow subgroups are s-c-permutably embedded. A series of known results are generalized.
MSC:
20D40 Products of subgroups of abstract finite groups
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D15 Finite nilpotent groups, \(p\)-groups
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Full Text: MNR