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Some new permutability properties of hypercentrally embedded subgroups of finite groups. (English) Zbl 1107.20018

A subgroup of a finite group \(G\) is hypercentrally embedded in \(G\) if it permutes with every pronormal subgroup of \(G\). In general, hypercentrally embedded subgroups do not permute with the intersection of two pronormal subgroups. Here, the authors show that they nevertheless permute with certain relevant subgroups that can be described as intersections of pronormal subgroups. These include for instance \(\mathfrak F\)-normalizers for a saturated formation \(\mathfrak F\) and subgroups of prefrattini type, which are intersections of maximal subgroups.

MSC:

20D40 Products of subgroups of abstract finite groups
20D30 Series and lattices of subgroups
20D25 Special subgroups (Frattini, Fitting, etc.)
20D35 Subnormal subgroups of abstract finite groups
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