Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T01:50:05.482Z Has data issue: false hasContentIssue false
  • English
  • Français

Soluble Groups with Finite Wielandt length

Published online by Cambridge University Press:  18 May 2009

Carlo Casolo
Carlo Casolo
Affiliation:
Dipartimento di Mathematica e Informatica, Università di Udine, Via Zanon, 6, I-33100 Udine, Italy
Rights & Permissions [Opens in a new window]

Extract

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.

The Wielandt subgroup ω(G) of a group G is defined to be the intersection of all normalizers of subnormal subgroups of G; the terms of the Wielandt series of G are defined, inductively, by putting ω0(G) = 1 and (ωn+1(G)/ωn(G) = ω(G/ωn(G)). If, for some integer n, ωn(G) = G, then G is said to have finite Wielandt length; the Wielandt length of G being the minimal n such that ωn(G) = G.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 3 , September 1989 , pp. 329 - 334
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

1.Bryce, R. A. and Cossey, J., The Wielandt subgroup of a finite soluble group. The Austral. Nat. Univ. MSRC-Research Report 2 (1988).Google Scholar
2.Camina, A., The Wielandt length of finite groups. J. Algebra 15 (1970), 142–148.CrossRefGoogle Scholar
3.Cooper, C. H., Power automorphisms of a group. Math. Z. 107 (1968), 335–356.CrossRefGoogle Scholar
4.Robinson, D. J. S., Groups in which normality is a transitive relation. Proc. Cambridge Phil. Soc. 60 (1964), 21–38.CrossRefGoogle Scholar
5.Robinson, D. J. S.. A Course in the Theory of Groups (Springer-Verlag, 1982).CrossRefGoogle Scholar
6.Robinson, D. J. S.. Finiteness Conditions and Generalized Soluble Groups (Springer-Verlag, 1972).CrossRefGoogle Scholar
7.Schenkman, E., On the Norm of a group, Ill. J. Math. 4 (1960), 150–152.Google Scholar
8.Wielandt, H., Über den Normalisator der subnormalen Untergruppen, Math. Z. 69 (1958), 463–465.CrossRefGoogle Scholar