Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 243–251 | Cite as

On the Group of Continuous Automorphisms of Some Profinite Groups

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Abstract

We prove some conditions on a given abstract group G, such that the group Aut c (\(\hat G\)) of the continuous automorphisms of the profinite completion \(\hat G\) of G endowed with the congruence subgroup topology, is profinite. Also, for a given abstract group G, if Aut c (\(\hat G\)) is profinite, then we establish relations betweenG, Aut(G), \(\widehat {Aut(G)}\), and Aut c (\(\hat G\)) when each of these groups is endowed with appropriate topology. Finally, we applied the obtained results to the class of one-relator groups given by the presentation G mn = 〈a, b; [a m , b n ] = 1〉 (m > 1,n > 1).

Keywords and phrases

Profinite groups profinite completions profinite topology congruence subgroup topology 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Ecole Normale SupérieureThe University of MarouaMarouaCameroon
  2. 2.Department of Mathematics and Computer ScienceThe University of NgaoundereNgaoundereCameroon

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