Article contents
Subgroups like Wielandt's in solublegroups
Published online by Cambridge University Press: 07 August 2001
Abstract
For each m≥1, u_{m}(G) is defined to be the intersection of the normalizers of all the subnormal subgroups of defect at most m in G. An ascending chain of subgroups u_{m,i}(G) is defined by setting u_{m,i}(G)/u_{m,i−1}(G)=u_{m}(G/u_{m,i−1}(G)). If u_{m,n}(G)=G, for some integer n, the m-Wielandt length of G is the minimal of such n.
In [3], Bryce examined the structure of a finite soluble group with given m-Wielandt length, in terms of its polynilpotent structure. In this paper we extend his results to infinite soluble groups.
1991 Mathematics Subject Classification. 20E15, 20F22.
- Type
- Research Article
- Information
- Copyright
- 2000 Glasgow Mathematical Journal Trust
- 2
- Cited by