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Lower central depth in finitely generated soluble-by-finite groups

Published online by Cambridge University Press:  18 May 2009

John C. Lennox
John C. Lennox
Affiliation:
Department of Pure Mathematics, University College, P.O. Box 78, Cardiff Cf1 1Xl
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We say that a group G has finite lower central depth (or simply, finite depth) if the lower central series of G stabilises after a finite number of steps.

In [1], we proved that if G is a finitely generated soluble group in which each two generator subgroup has finite depth then G is a finite-by-nilpotent group. Here, in answer to a question of R. Baer, we prove the following stronger version of this result.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 2 , July 1978 , pp. 153 - 154
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

REFERENCES

1.Lennox, J. C., Finitely generated soluble groups in which all subgroups have finite lower central depth, Bull. London Math. Soc. 7 (1975), 273–278.Google Scholar
2.Peng, T. A., Engel elements of groups with maximal condition on abelian subgroups, Nanta Math. 1 (1966), 23–28.Google Scholar
3.Robinson, D. J. S., Finiteness conditions and generalised soluble groups, Vol II (Springer, 1972).Google Scholar