On the Group of Continuous Automorphisms of Some Profinite Groups
- Autores: Mantika G.1, Tieudjo D.2
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Afiliações:
- Department of Mathematics, Ecole Normale Supérieure
- Department of Mathematics and Computer Science
- Edição: Volume 39, Nº 2 (2018)
- Páginas: 243-251
- Seção: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/201524
- DOI: https://doi.org/10.1134/S1995080218020191
- ID: 201524
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Resumo
We prove some conditions on a given abstract group G, such that the group Autc(\(\hat G\)) 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 Autc(\(\hat G\)) is profinite, then we establish relations betweenG, Aut(G), \(\widehat {Aut(G)}\), and Autc(\(\hat G\)) 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 Gmn = 〈a, b; [am, bn] = 1〉 (m > 1,n > 1).
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Sobre autores
Gilbert Mantika
Department of Mathematics, Ecole Normale Supérieure
Autor responsável pela correspondência
Email: gilbertmantika@yahoo.fr
Camarões, Maroua
Daniel Tieudjo
Department of Mathematics and Computer Science
Email: gilbertmantika@yahoo.fr
Camarões, Ngaoundere