Khukhro, E. I. (2009) On solubility of groups with bounded centralizer chains. Glasgow Math. J., 51. pp. 49-54.
![[thumbnail of eart075.pdf]](https://eprints.maths.manchester.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
eart075.pdf Download (180kB) |
Abstract
The $c$-dimension of a group is the maximum length of a chain of nested centralizers. It is proved that a periodic locally soluble group of finite $c$-dimension $k$ is soluble of derived length bounded in terms of~$k$, and the rank of its quotient by the Hirsch--Plotkin radical is bounded in terms of~$k$. Corollary: a pseudo-(finite soluble) group of finite $c$-dimension $k$ is soluble of derived length bounded in terms of~$k$.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | centralizer lattice; derived length; pseudofinite groups |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations |
| Depositing User: | Professor Evgeny Khukhro |
| Date Deposited: | 18 Oct 2012 |
| Last Modified: | 20 Oct 2017 14:13 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1892 |
Actions (login required)
 |
View Item |