@article{f5e3691075284483b8a5b3c576861d27,
title = "Characterization of solvable groups and solvable radical",
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.",
keywords = "Solvable group, algebraic variety, finite field, simple group, solvable radical",
author = "Fritz Grunewald and Boris Kunyavskii and Eugene Plotkin",
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-Universit{\"a}t (D{\"u}sseldorf).",
year = "2013",
month = aug,
doi = "https://doi.org/10.1142/S0218196713300016",
language = "الإنجليزيّة",
volume = "23",
pages = "1011--1062",
journal = "International Journal of Algebra and Computation",
issn = "0218-1967",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "5",
}