Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T16:39:49.565Z Has data issue: false hasContentIssue false
  • English
  • Français

A Jordan-Hölder Theorem for Finitary Groups

Published online by Cambridge University Press:  20 November 2018

B. A. F. Wehrfritz
B. A. F. Wehrfritz*
Affiliation:
School of Mathematical Sciences, Queen Mary & Westfield College, Mile End Road, London E1 4NS, England
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let V be any left vector space over any division ring D and let G be any group of finitary linear maps of V. Then the D — G bimodule V satisfies a Jordan- Hölder theorem. Specifically, there is a bijection between the G-nontrivial factors in two composition series of V such that corresponding factors are isomorphic as D — G bimodules. This cannot be extended to cover the G-trivial factors.

Keywords

20H9916K99groupfinitarycomposition series
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 2 , 01 June 1995 , pp. 250 - 251
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Kegel, O. H. and Wehrfritz, B. A. F., Locally Finite Groups, North-Holland, Amsterdam, 1973.Google Scholar
2. Robinson, D. J. S., Finiteness Conditions and Generalized Soluble Groups Vol. 1, Springer-Verlag, Berlin, 1972.Google Scholar
3. Wehrfritz, B. A. F., Locally soluble finitary skew linear groups, J. Algebra 160(1993), 226–241.Google Scholar