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.
Accepted:
Published online:
Tatiana Bandman 1; Gert-Martin Greuel 2; Fritz Grunewald 3; Boris Kunyavskiı̆ 1; Gerhard Pfister 2; Eugene Plotkin 1
@article{CRMATH_2003__337_9_581_0,
author = {Tatiana Bandman and Gert-Martin Greuel and Fritz Grunewald and Boris Kunyavski{\i}̆ and Gerhard Pfister and Eugene Plotkin},
title = {Two-variable identities for finite solvable groups},
journal = {Comptes Rendus. Math\'ematique},
pages = {581--586},
publisher = {Elsevier},
volume = {337},
number = {9},
year = {2003},
doi = {10.1016/j.crma.2003.09.003},
language = {en},
}
TY - JOUR AU - Tatiana Bandman AU - Gert-Martin Greuel AU - Fritz Grunewald AU - Boris Kunyavskiı̆ AU - Gerhard Pfister AU - Eugene Plotkin TI - Two-variable identities for finite solvable groups JO - Comptes Rendus. Mathématique PY - 2003 SP - 581 EP - 586 VL - 337 IS - 9 PB - Elsevier DO - 10.1016/j.crma.2003.09.003 LA - en ID - CRMATH_2003__337_9_581_0 ER -
%0 Journal Article %A Tatiana Bandman %A Gert-Martin Greuel %A Fritz Grunewald %A Boris Kunyavskiı̆ %A Gerhard Pfister %A Eugene Plotkin %T Two-variable identities for finite solvable groups %J Comptes Rendus. Mathématique %D 2003 %P 581-586 %V 337 %N 9 %I Elsevier %R 10.1016/j.crma.2003.09.003 %G en %F CRMATH_2003__337_9_581_0
Tatiana Bandman; Gert-Martin Greuel; Fritz Grunewald; Boris Kunyavskiı̆; Gerhard Pfister; Eugene Plotkin. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.09.003/
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