2002•Mathematische NachrichtenRequires access

A Characterization of the Class of Finite Groups with Nilpotent Derived Subgroup

A. Ballester‐Bolinches, Luis M. Ezquerro, M. C. Pedraza-Aguilera

Abstract

The class of all finite groups with nilpotent commutator subgroup is characterized as the largest subgroup-closed saturated formation 𝔉 for which the 𝔉-residual of a group generated by two 𝔉-subnormal subgroups is the subgroup generated by their 𝔉–residuals.

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Key concepts: Mathematics, Commutator subgroup, Fitting subgroup, Characteristic subgroup, Omega and agemo subgroup, Nilpotent, Normal subgroup, Class (philosophy)