Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T07:46:32.186Z Has data issue: false hasContentIssue false
  • English
  • Français

Central series in wreath products

Published online by Cambridge University Press:  24 October 2008

J. D. P. Meldrum
J. D. P. Meldrum
Affiliation:
Emmanuel College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper we study the structure of the α-central series of the nilpotent wreath product of two Abelian groups, the α-central series being the intersection of the upper central series with the base group. Let C = A wr B, the standard restricted wreath product of A and B. Then Baumslag(1) showed that C is nilpotent if and only if A is a nilpotent p-group of finite exponent and B is a finite p-group for the same prime p. In (5) Liebeck calculated the nilpotency class of the nilpotent wreath product of two Abelian groups. We obtain an expression for an element of the base group to belong to a given term of the upper central series.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 551 - 567
Copyright
Copyright © Cambridge Philosophical Society 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Baumslag, G.Wreath products and p-groups. Proc. Cambridge Philos. Soc. 55 (1959), 224–231.CrossRefGoogle Scholar
(2)Fuchs, L.Abelian groups (Pergamon Press, 1960).Google Scholar
(3)Hall, P.Nilpotent groups (Canadian Mathematical Congress, 1957).Google Scholar
(4)Kurosh, A. G.The theory of groups, vols. 1 and 2 (Chelsea, 1956).Google Scholar
(5)Liebeck, H.Concerning nilpotent wreath products. Proc. Cambridge Philos. Soc. 58 (1962), 443–451.CrossRefGoogle Scholar
(6)Neumann, P. M.On the structure of standard wreath products of groups. Math. Z. 84 (1964), 343–373.CrossRefGoogle Scholar