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RESEARCH PRODUCT
On a theorem of Berkovich
Manuel J. AlejandreAdolfo Ballester-bolinchessubject
AlgebraMathematics::Group TheoryNilpotentPure mathematicsProperty (philosophy)Group (mathematics)General MathematicsStructure (category theory)Nilpotent groupType (model theory)Central seriesResidualMathematicsdescription
In a recent paper, Berkovich studied how to describe the nilpotent residual of a group in terms of the nilpotent residuals of some of its subgroups. That study required the knowledge of the structure of the minimal nonnilpotent groups, also called Schmidt groups. The major aim of this paper is to show that this description could be obtained as a consequence of a more complete property, giving birth to some interesting generalizations. This purpose naturally led us to the study of a family of subgroup-closed saturated formations of nilpotent type. An innovative approach to these classes is provided.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-12-01 | Israel Journal of Mathematics |