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Subgroups like Wielandt's in solublegroups

Published online by Cambridge University Press:  07 August 2001

Clara Franchi
Clara Franchi
Affiliation:
Dipartimento di Matematica pura ed applicata, Università di Padova, Via Belzoni, 7, I-35131 Padova, Italy
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Abstract

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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
Glasgow Mathematical Journal , Volume 42 , Issue 1 , March 2000 , pp. 67 - 74
Copyright
2000 Glasgow Mathematical Journal Trust