Characterization of solvable groups and solvable radical

Fritz Grunewald; Boris Kunyavskii; Eugene Plotkin

doi:10.1142/S0218196713300016

Characterization of solvable groups and solvable radical

Fritz Grunewald, Boris Kunyavskii, Eugene Plotkin

Department of Mathematics

Heinrich Heine University Düsseldorf

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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 language	English
Pages (from-to)	1011-1062
Number of pages	52
Journal	International Journal of Algebra and Computation
Volume	23
Issue number	5
DOIs	https://doi.org/10.1142/S0218196713300016
State	Published - 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).

Keywords

Solvable group
algebraic variety
finite field
simple group
solvable radical

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10.1142/S0218196713300016

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author = "Fritz Grunewald and Boris Kunyavskii and Eugene Plotkin",

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Characterization of solvable groups and solvable radical

Abstract

Bibliographical note

Keywords

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