Abstract
We describe generalised soluble or nilpotent groups G in which, for all H ≤ G, the group of outer automorphisms induced on H by elements of G via conjugation (that is, the factor N G (H)/HC G (H)) is finite. It turns out that such groups are abelian-by-finite; the nilpotent ones are centre-by-finite. Also groups in which the same condition is imposed on abelian subgroups only are considered.
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