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G. Cutolo
Groups with finite outer automizers
Comm. Algebra, 40, (2012), pp. 1293–1303.
doi: 10.1080/00927872.2010.550902
MathSciNet Zentralblatt Abstract Full Text
Abstract
We describe generalised soluble or nilpotent groups $G$ in which, for all $H\le G$, 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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