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.
On groups with all subgroups almost subnormal
DETOMI, ELOISA MICHELA
2004
Abstract
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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