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Centre-by-metabelian pro-p groups of type FPm

Published online by Cambridge University Press:  01 September 2008

DESSISLAVA H. KOCHLOUKOVA  and
ALINE G. S. PINTO
DESSISLAVA H. KOCHLOUKOVA
Affiliation:
Department of Mathematics, University of Campinas (UNICAMP), Cx. P. 6065, 13083-970 Campinas - SP, Brazil.
ALINE G. S. PINTO
Affiliation:
Department of Mathematics, University of Campinas (UNICAMP), Cx. P. 6065, 13083-970 Campinas - SP, Brazil.
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Abstract

We prove that if G is a centre-by-metabelian pro-p group of type FPm over , so every homomorphic image of G is of type FPm over .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 2 , September 2008 , pp. 305 - 309
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

REFERENCES

[1]Bieri, R. and Strebel, R.. Valuations and finite presented metabelian groups. Proc. London Math. Soc. (3) 41 (1980), 439–464.CrossRefGoogle Scholar
[2]Bieri, R. and Groves, J. R. J.. Metabelian groups of type (FP)∞ are virtually of type (FP). Proc. London Math. Soc. (3) 45 (1982), no. 2, 365–384.CrossRefGoogle Scholar
[3]Bryant, R. M. and Groves, J. R. J.. Finitely presented centre-by-metabelian Lie algebras. Bull. Austral. Math. Soc. 60 (1999), no. 2, 221–226.CrossRefGoogle Scholar
[4]Dixon, J., Sautoy, M. du, Mann, A. and Segal, D.. Analytic pro-p groups. London Math. Soc. Lecture Notes Series 157 (Cambridge University Press, 1991).Google Scholar
[5]Groves, J. R. J. and Kochloukova, D. H.. Embeddings properties of metabelian Lie algebras and metabelian discrete groups. J. London Math. Soc. (2) 73 (2006), no. 2, 475–492.CrossRefGoogle Scholar
[6]King, J.. Embedding theorems for pro-p groups. Math. Proc. Camb. Phil. Soc. 123 (1998), no. 2, 217–226.CrossRefGoogle Scholar
[7]King, J.. Homological finiteness conditions for pro-p groups. Comm. Algebra 27 (1999), no. 10, 4969–4991.CrossRefGoogle Scholar
[8]King, J.. A geometric invariant for metabelian pro-p groups. J. London Math. Soc. (2) 60 (1999), no. 1, 83–94.CrossRefGoogle Scholar
[9]Kochloukova, D. H.. Metabelian pro-p groups of type FPm. J. Group Theory 3 (2000), no. 4, 419–431.CrossRefGoogle Scholar
[10]Kochloukova, D. H. and Pinto, A. G. S.. Embedding properties of metabelian pro-p groups. J. Group Theory 9 (2006), no. 4, 455–465.CrossRefGoogle Scholar
[11]Kochloukova, D. H. and Zalesskii, P.. Invariants for pro-p groups and some finitely presented pro-C groups. Monatsh. Math. 144 (2005), 285–296.CrossRefGoogle Scholar
[12]Pletch, A.. Profinite duality groups I. J. Pure Appl. Algebra 16 (1980), 55–74, 285–297.CrossRefGoogle Scholar
[13]Ribes, L. and Zalesskii, P.. Profinite groups (Springer-Verlag, 2000).CrossRefGoogle Scholar