Hostname: page-component-84b7d79bbc-4hvwz Total loading time: 0 Render date: 2024-07-29T22:52:12.440Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on a centrality property of finitely generated soluble groups

Published online by Cambridge University Press:  24 October 2008

J. C. Lennox
J. C. Lennox
Affiliation:
Department of Pure Mathematics, University College, P.O. Box 78, Cardiff CFI 1XL, Great Britain
Get access Rights & Permissions [Opens in a new window]

Extract

We recall from (3) that a group G is (centrally) eremitic if there exists a positive integer e such that, whenever an element of G has some power in a centralizer, it has its eth power. The eccentricity of an eremitic group G is the least such positive integer e.

In ((4), Theorem A) we proved that if A is a torsion free Abelian normal subgroup of a finitely generated group G with G/A nilpotent, then G has a subgroup of finite index with eccentricity 1. In this note we use a much simpler method to prove a stronger result.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 1 , January 1974 , pp. 23 - 24
Copyright
Copyright © Cambridge Philosophical Society 1974

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)Hall, P.Finiteness conditions in soluble groups. Proc. London Math. Soc. (3), 4 (1954), 419–436.Google Scholar
(2)Kurosh, A. G.Theory of Groups, vol. 2 (Chelsea; New York, 1961).Google Scholar
(3)Lennox, J. C. and Roseblade, J. E.Centrality in finitely generated soluble groups, J. Algebra 16 (1970), 399–438.CrossRefGoogle Scholar
(4)Lnnox, J. C.On a centrality property of finitely generated torsion free soluble groups. J. Algebra 18 (1971), 541–548.CrossRefGoogle Scholar