Group Theory/Algebraic Geometry
Two-variable identities for finite solvable groups
Comptes Rendus. Mathématique, Volume 337 (2003) no. 9, pp. 581-586.

We characterise the solvable groups in the class of finite groups by an inductively defined sequence of two-variable identities. Our main theorem is the analogue of a classical theorem of Zorn which gives a characterisation of the nilpotent groups in the class of finite groups by a sequence of two-variable identities.

On caractérise les groupes résolubles dans la classe des groupes finis par une suite d'identités en deux variables définies par récurrence. Le résultat principal peut être considéré comme l'analogue du théorème classique de Zorn qui donne une caractérisation des groupes nilpotents dans la classe des groupes finis par une suite d'identités en deux variables.

Published online:
DOI: 10.1016/j.crma.2003.09.003
Bandman, Tatiana 1; Greuel, Gert-Martin 2; Grunewald, Fritz 3; Kunyavskiı̆, Boris 1; Pfister, Gerhard 2; Plotkin, Eugene 1

1 Department of Mathematics and Statistics, Bar-Ilan University, 52900 Ramat Gan, Israel
2 Fachbereich Mathematik, Universität Kaiserslautern, 67653 Kaiserslautern, Germany
3 Mathematisches Institut, Heinrich Heine Universität, 40225 Düsseldorf, Germany
     author = {Bandman, Tatiana and Greuel, Gert-Martin and Grunewald, Fritz and Kunyavski{\i}̆, Boris and Pfister, Gerhard and Plotkin, Eugene},
     title = {Two-variable identities for finite solvable groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {581--586},
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Bandman, Tatiana; Greuel, Gert-Martin; Grunewald, Fritz; Kunyavskiı̆, Boris; Pfister, Gerhard; Plotkin, Eugene. Two-variable identities for finite solvable groups. Comptes Rendus. Mathématique, Volume 337 (2003) no. 9, pp. 581-586. doi : 10.1016/j.crma.2003.09.003.

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