[Identités en deux variables pour les groupes résolubles finis]
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.
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.
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@article{CRMATH_2003__337_9_581_0,
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},
publisher = {Elsevier},
volume = {337},
number = {9},
year = {2003},
doi = {10.1016/j.crma.2003.09.003},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2003.09.003/}
}
TY - JOUR AU - Bandman, Tatiana AU - Greuel, Gert-Martin AU - Grunewald, Fritz AU - Kunyavskiı̆, Boris AU - Pfister, Gerhard AU - Plotkin, Eugene TI - Two-variable identities for finite solvable groups JO - Comptes Rendus. Mathématique PY - 2003 SP - 581 EP - 586 VL - 337 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2003.09.003/ DO - 10.1016/j.crma.2003.09.003 LA - en ID - CRMATH_2003__337_9_581_0 ER -
%0 Journal Article %A Bandman, Tatiana %A Greuel, Gert-Martin %A Grunewald, Fritz %A Kunyavskiı̆, Boris %A Pfister, Gerhard %A Plotkin, Eugene %T Two-variable identities for finite solvable groups %J Comptes Rendus. Mathématique %D 2003 %P 581-586 %V 337 %N 9 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2003.09.003/ %R 10.1016/j.crma.2003.09.003 %G en %F CRMATH_2003__337_9_581_0
Bandman, Tatiana; Greuel, Gert-Martin; Grunewald, Fritz; Kunyavskiı̆, Boris; Pfister, Gerhard; Plotkin, Eugene. Two-variable identities for finite solvable groups. Comptes Rendus. Mathématique, Tome 337 (2003) no. 9, pp. 581-586. doi : 10.1016/j.crma.2003.09.003. http://archive.numdam.org/articles/10.1016/j.crma.2003.09.003/
[1] On the degree of the L-functions associated with an exponential sum, Compositio Math., Volume 68 (1998), pp. 125-159
[2] Dynamics of implicit operations and tameness of pseudovarieties of groups, Trans. Amer. Math. Soc., Volume 354 (2002), pp. 387-411
[3] Zur Theorie der untergruppenabgeschlossenen Formationen: endliche Varietäten, J. Algebra, Volume 73 (1981), pp. 1-22
[4] Characterization of finite soluble groups by laws in a small number of variables, J. Algebra, Volume 116 (1988), pp. 334-341
[5] Rigid geometry, Lefschetz–Verdier trace formula and Deligne's conjecture, Invent. Math., Volume 127 (1997), pp. 480-533
[6] Étale cohomology, Lefschetz theorems and number of points of singular varieties over finite fields, Moscow Math. J., Volume 2 (2002), pp. 589-631
[7] A SINGULAR Introduction to Commutative Algebra, Springer-Verlag, Berlin, 2002
[8] Two-variable identities in groups and Lie algebras, J. Math. Sci. (New York), Volume 272 (2000), pp. 161-176
[9] Finite Groups, III, Springer-Verlag, Berlin, 1982
[10] Generalized soluble and generalized nilpotent groups, Uspekhi Mat. Nauk, Volume 13 (1958) no. 4, pp. 89-172 English translation: Amer. Math. Soc. Transl. (2), 17, 1961, pp. 29-115
[11] Non-solvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc., Volume 74 (1968), pp. 383-437
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