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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 eachm≥1, u_{m}(G) is defined to be theintersection of the normalizers of all the subnormal subgroups of defect at mostm in G. An ascending chain of subgroupsu_{m,i}(G) is defined by settingu_{m,i}(G)/u_{m,i−1}(G)=u_{m}(G/u_{m,i−1}(G)). Ifu_{m,n}(G)=G, for some integer n, them-Wielandt length of G is theminimal of such n.

In [3], Bryce examined thestructure of a finite soluble group with given m-Wielandtlength, in terms of its polynilpotent structure. In this paper we extend hisresults to infinite soluble groups.

1991 Mathematics SubjectClassification. 20E15, 20F22.

Information

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