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The Quarterly Journal of Mathematics Advance Access originally published online on October 26, 2006
The Quarterly Journal of Mathematics 2007 58(1):47-51; doi:10.1093/qmath/hal018
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© 2006. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

AUTOMORPHISMS OF PRO-p GROUPS OF FINITE VIRTUAL COHOMOLOGICAL DIMENSION

Dessislava H. Kochloukova1,{dagger} § and Pavel A. Zalesskii2 {ddagger} §

1 UNICAMP-IMECC, Cx. P. 6065, 13083-970 Campinas, SP, Brazil
2 Department of Mathematics, University of Brasilia, 70910-900 DF, Brazil

{dagger} E-mail: desi{at}ime.unicamp.br

Received 6 February 2006;
  Abstract

Let G be a pro-p group of finite cohomological dimension and type FP{infty} and T be a finite p-group of automorphisms of G. We prove that the group of fixed points of T in G is again a pro-p group of type FP{infty} (in particular it is finitely presented). Moreover, we prove that a pro-p group G of type FP{infty} and finite virtual cohomological dimension has finitely many conjugacy classes of finite subgroups.

{ddagger} E-mail: pz{at}mat.unb.br

§ Both authors are partially supported by ‘bolsa de produtividade de pesquisa’ from CNPq, Brazil.


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