We are looking for the smallest integer providing the following characterization of the solvable radical of any finite group G: consists of the elements g such that for any k elements the subgroup generated by the elements , , is solvable. Our method is based on considering a similar problem for commutators: find the smallest integer with the property that consists of the elements g such that for any ℓ elements the subgroup generated by the commutators , , is solvable.
Nous cherchons le plus petit entier caractérisant le radical résoluble d'un groupe fini G comme suit : est l'ensemble des éléments g tels que pour toute partie à k éléments le sous-groupe engendré par les élements , , est résoluble. Notre méthode s'appuie sur la considération d'un problème similaire pour les commutateurs. Nous cherchons le plus petit entier ayant la propriété suivante : est l'ensemble des éléments g tels que pour toute partie à ℓ éléments le sous-groupe engendré par les commutateurs , , est résoluble.
Accepted:
Published online:
Nikolai Gordeev 1; Fritz Grunewald 2; Boris Kunyavskiĭ 3; Eugene Plotkin 3
@article{CRMATH_2006__343_6_387_0, author = {Nikolai Gordeev and Fritz Grunewald and Boris Kunyavski\u{i} and Eugene Plotkin}, title = {On the number of conjugates defining the solvable radical of a finite group}, journal = {Comptes Rendus. Math\'ematique}, pages = {387--392}, publisher = {Elsevier}, volume = {343}, number = {6}, year = {2006}, doi = {10.1016/j.crma.2006.08.005}, language = {en}, }
TY - JOUR AU - Nikolai Gordeev AU - Fritz Grunewald AU - Boris Kunyavskiĭ AU - Eugene Plotkin TI - On the number of conjugates defining the solvable radical of a finite group JO - Comptes Rendus. Mathématique PY - 2006 SP - 387 EP - 392 VL - 343 IS - 6 PB - Elsevier DO - 10.1016/j.crma.2006.08.005 LA - en ID - CRMATH_2006__343_6_387_0 ER -
%0 Journal Article %A Nikolai Gordeev %A Fritz Grunewald %A Boris Kunyavskiĭ %A Eugene Plotkin %T On the number of conjugates defining the solvable radical of a finite group %J Comptes Rendus. Mathématique %D 2006 %P 387-392 %V 343 %N 6 %I Elsevier %R 10.1016/j.crma.2006.08.005 %G en %F CRMATH_2006__343_6_387_0
Nikolai Gordeev; Fritz Grunewald; Boris Kunyavskiĭ; Eugene Plotkin. On the number of conjugates defining the solvable radical of a finite group. Comptes Rendus. Mathématique, Volume 343 (2006) no. 6, pp. 387-392. doi : 10.1016/j.crma.2006.08.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.08.005/
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