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On finite \(p\)-groups of supersoluble type. (English) Zbl 07282587
Summary: A finite \(p\)-group \(S\) is said to be of supersoluble type if every fusion system over \(S\) is supersoluble. The main aim of this paper is to characterise the finite \(p\)-groups of supersoluble type. Abelian and metacyclic \(p\)-groups of supersoluble type are completely described. Furthermore, we show that the Sylow \(p\)-subgroups of supersoluble type of a finite simple group must be cyclic.
MSC:
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D15 Finite nilpotent groups, \(p\)-groups
20D05 Finite simple groups and their classification
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