Alexander Brudnyi,Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4; e-mail: abrudnyi@ucalgary.ca

Abstract/Résumé:

We study the structure of countable subgroups of the group \(G[[r]]\) of complex formal power series under the operation of composition of series. In particular, we prove that every finitely generated fully residually free group is embeddable in \(G[[r]]\)

Nous étudions la structure des sous-groupes dénombrables du groupe \(G[[r]]\)des séries de puissance formelle sous l’opération de la composition des séries. En particulier, nous prouvons que chaque groupe qui est finement engendré et \(\omega\)-résiduellement libre admet un plongement dans \(G[[r]]\)

Keywords: Group of formal power series, free product of groups, fully residually free group, the big powers condition

AMS Subject Classification: Free products; free products with amalgamation; Higman-Neumann-Neumann extensions; and generalizations, Other groups related to topology or analysis 20E06, 20F38

PDF(click to download): Subgroups of the Group of Formal Power Series with the Big Powers Condition