Thompson-like characterization of the solvable radical
Group Theory
2008-01-03 v2
Abstract
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.
Cite
@article{arxiv.math/0504176,
title = {Thompson-like characterization of the solvable radical},
author = {R. Guralnick and B. Kunyavskii and E. Plotkin and A. Shalev},
journal= {arXiv preprint arXiv:math/0504176},
year = {2008}
}
Comments
13 pages; completely revised and extended version