Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T14:15:44.803Z Has data issue: false hasContentIssue false
  • English
  • Français

Completions of certain nilpotent groups

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Siegfried Moran  and
Janet Williams
Siegfried Moran
Affiliation:
The University CanterburyKent, United Kingdom
Janet Williams
Affiliation:
The University CanterburyKent, United Kingdom
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.

The completions of certain nilpotent groups with respect to some ascending sequences of integral domains are constructed. These completions are generalizations of Lazard completions for the groups under consideration and they are Lie algebras over the first integral domain in the sequence. The construction is possible in particular for finite p-groups of exponent p and class < p.

MSC classification

Secondary: 20E15: Chains and lattices of subgroups, subnormal subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 4 , December 1979 , pp. 461 - 470
Copyright
Copyright © Australian Mathematical Society 1979

References

Referneces

Duguid, A. M. (1957), Some generalizations of nilpotent groups (Ph.D. Thesis, University of Cambridge).Google Scholar
Hall, M. (1959), The theory of groups (Macmillan, New York).Google Scholar
Hall, P. (1957), Nilpotent groups (Canadian Mathematical Congress Notes).Google Scholar
Lazard, M. (1954), ‘Sur les groupes nilpotents et les anneaux de Lie’, Ann. Sci. École Norm. Sup. (3) 71, 101–190.CrossRefGoogle Scholar
Moran, S. (1973), ‘Some subalgebra theorems’, J. Algebra 27, 366–371.CrossRefGoogle Scholar
Warfield, R. B. Jr (1976), Nilpotent groups (Lecture Notes in Mathematics 513, Springer-Verlag, Berlin).CrossRefGoogle Scholar