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 NG(H)/HCG(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.
Groups with finite outer automizers / Cutolo, Giovanni. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - 40:4(2012), pp. 1293-1303. [10.1080/00927872.2010.550902]
Groups with finite outer automizers
CUTOLO, GIOVANNI
2012
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 NG(H)/HCG(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.File in questo prodotto:
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