Two-variable identities for finite solvable groups Identités en deux variables pour les groupes résolubles finis

Tatiana Bandman; Gert Martin Greuel; Fritz Grunewald; Boris Kunyavskiǐ; Gerhard Pfister; Eugene Plotkin

doi:10.1016/j.crma.2003.09.003

Two-variable identities for finite solvable groups Identités en deux variables pour les groupes résolubles finis

Translated title of the contribution: Two-variable identities for finite solvable groups

Tatiana Bandman, Gert Martin Greuel, Fritz Grunewald, Boris Kunyavskiǐ, Gerhard Pfister, Eugene Plotkin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

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.

Translated title of the contribution	Two-variable identities for finite solvable groups
Original language	English
Pages (from-to)	581-586
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	337
Issue number	9
DOIs	https://doi.org/10.1016/j.crma.2003.09.003
State	Published - 1 Nov 2003

Bibliographical note

Funding Information:
Bandman, Kunyavski˘ı, and Plotkin were partially supported by the Ministry of Absorption (Israel), the Israeli Science Foundation founded by the Israeli Academy of Sciences – Center of Excellence Program, and the Minerva Foundation through the Emmy Noether Research Institute of Mathematics. Kunyavski˘ı and Plotkin were also supported by the RTN network HPRN-CT-2002-00287 and INTAS 00-566. Greuel and Pfister were partially supported by the DFG project “Globale Methoden in der komplexen Geometrie” as well as by the Stiftung Rheinland–Pfalz für Innovation. Greuel was also supported by the German–Israeli Foundation for Scientific Research and Development, G-616-15.6/1999.

Funding

Bandman, Kunyavski˘ı, and Plotkin were partially supported by the Ministry of Absorption (Israel), the Israeli Science Foundation founded by the Israeli Academy of Sciences – Center of Excellence Program, and the Minerva Foundation through the Emmy Noether Research Institute of Mathematics. Kunyavski˘ı and Plotkin were also supported by the RTN network HPRN-CT-2002-00287 and INTAS 00-566. Greuel and Pfister were partially supported by the DFG project “Globale Methoden in der komplexen Geometrie” as well as by the Stiftung Rheinland–Pfalz für Innovation. Greuel was also supported by the German–Israeli Foundation for Scientific Research and Development, G-616-15.6/1999.

Funders	Funder number
Israeli Academy of Sciences
Ministry of Absorption
RTN	HPRN-CT-2002-00287, INTAS 00-566
Minerva Foundation
Deutsche Forschungsgemeinschaft
German-Israeli Foundation for Scientific Research and Development	G-616-15.6/1999
Israel Science Foundation
Stiftung Rheinland-Pfalz für Innovation

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10.1016/j.crma.2003.09.003

Cite this

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title = "Two-variable identities for finite solvable groups Identit{\'e}s en deux variables pour les groupes r{\'e}solubles finis",

abstract = "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.",

author = "Tatiana Bandman and Greuel, {Gert Martin} and Fritz Grunewald and Boris Kunyavskiǐ and Gerhard Pfister and Eugene Plotkin",

note = "Funding Information: Bandman, Kunyavski˘ı, and Plotkin were partially supported by the Ministry of Absorption (Israel), the Israeli Science Foundation founded by the Israeli Academy of Sciences – Center of Excellence Program, and the Minerva Foundation through the Emmy Noether Research Institute of Mathematics. Kunyavski˘ı and Plotkin were also supported by the RTN network HPRN-CT-2002-00287 and INTAS 00-566. Greuel and Pfister were partially supported by the DFG project “Globale Methoden in der komplexen Geometrie” as well as by the Stiftung Rheinland–Pfalz f{\"u}r Innovation. Greuel was also supported by the German–Israeli Foundation for Scientific Research and Development, G-616-15.6/1999.",

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AU - Pfister, Gerhard

AU - Plotkin, Eugene

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Two-variable identities for finite solvable groups Identités en deux variables pour les groupes résolubles finis

Abstract

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