J. Aust. Math. Soc.  77 (2004), 165-174
On groups with all subgroups almost subnormal

Eloisa Detomi
  Dipartimento di Matematica
  Facoltà di Ingegneria
  Università degli Studi di Brescia
  via Valotti 9
  25133 Brescia

In this paper we consider groups in which every subgroup has finite index in the  n th term of its normal closure series, for a fixed integer  n. We prove that such a group is the extension of a finite normal subgroup by a nilpotent group, whose class is bounded in terms of  n  only, provided it is either periodic or torsion-free.
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