Thompson-like characterization of the solvable radical

Details Thompson-like characterization of the solvable radical Thompson-like characterization of the solvable radical

2005-04-08

arxiv.org/abs/math/0504176v2

J. Algebra 300 (2006), 363-375

Mathematics

Group Theory

13 pages; completely revised and extended version

Scientific paper

We prove that the solvable radical of a finite group G coincides with the set
of elements y having the following property: for any x in G the subgroup of G
generated by x and y is solvable. We present analogues of this result for
finite dimensional Lie algebras and some classes of infinite groups. We also
consider a similar problem for pairs of elements.

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