A subgroup X of a group G is said to be transitively normal if X is normal in any subgroup Y of G such that X≤Y and X is subnormal in Y. We investigate the structure of generalised soluble groups with dense transitively normal subgroups, that is, groups in which every nonempty open interval in their subgroup lattice contains a transitively normal subgroup. In particular, it will be proved that nonperiodic generalised soluble groups with dense transitively normal subgroups are abelian.
Groups with dense transitively normal subgroups
Alessio Russo
In corso di stampa
Abstract
A subgroup X of a group G is said to be transitively normal if X is normal in any subgroup Y of G such that X≤Y and X is subnormal in Y. We investigate the structure of generalised soluble groups with dense transitively normal subgroups, that is, groups in which every nonempty open interval in their subgroup lattice contains a transitively normal subgroup. In particular, it will be proved that nonperiodic generalised soluble groups with dense transitively normal subgroups are abelian.File in questo prodotto:
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