Abstract
This chapter is a bit of a hotch-potch. In the first part we give an account of Platonov’s proof [43] of the nilpotence of the Frattini subgroup of a finitely generated linear group (4.17). Its main ingredient is a generalization (10.4) of Mal’cev’s Theorem (4.2) on the residual finiteness of a finitely generated linear group. This result is, I think, of independent interest and may well have many applications yet to be discovered. It will enable us to give, for example, an elementary proof of another result of Platonov on linear groups of finite rank ([46 b]). We also include in this section some simple structure theorems, taken from [69 c], for linear groups satisfying certain 2-generator solubility conditions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1973 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wehrfritz, B.A.F. (1973). Rank Restrictions, Varietal Properties and Wreath Products. In: Infinite Linear Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 76. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87081-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-87081-1_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-87083-5
Online ISBN: 978-3-642-87081-1
eBook Packages: Springer Book Archive