Characterization of solvable groups and solvable radical

Fritz Grunewald, Boris Kunyavskii, Eugene Plotkin

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6 Scopus citations


We give a survey of new characterizations of finite solvable groups and the solvable radical of an arbitrary finite group which were obtained over the past decade. We also discuss generalizations of these results to some classes of infinite groups and their analogues for Lie algebras. Some open problems are discussed as well.

Original languageEnglish
Pages (from-to)1011-1062
Number of pages52
JournalInternational Journal of Algebra and Computation
Issue number5
StatePublished - Aug 2013

Bibliographical note

Funding Information:
Kunyavski˘ı and Plotkin were supported in part by the Ministry of Absorption (Israel) and by the Israel Science Foundation, grant 1207/12. A substantial part of this work was done during their visits to MPIM (Bonn) in 2009 (supported in part by the Minerva Foundation through the Emmy Noether Research Institute of Mathematics) and the visit of Grunewald to the Hebrew University of Jerusalem in 2010, and discussed by all the coauthors during the international workshop (2009) hosted by the Heinrich-Heine-Universität (Düsseldorf).


  • Solvable group
  • algebraic variety
  • finite field
  • simple group
  • solvable radical


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