Driss Abouabdillah
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Driss Abouabdillah (Arabic: ادريس أبو عبدالله) (or Driss Bouabdillah) is a contemporary Moroccan mathematician born in Meknès on April 1, 1948. He is a teacher of algebra and geometry at the ENS (higher teacher training school) of Rabat.
[edit] Contributions
- In geometry, he gave several characterizations of similarities as mappings that preserve circles or spheres [1].
- He proposed an alternative axiomatic approach to Euclidean geometry by giving an axiomatic definition of equipollence. [2]
- He studied maximal sub-groups of the group of positive isometries and gave several examples of such subgroups.
- He also contributes to Abelian Group Theory and to Commutative Algebra where he gave the definition of topologically prüferian rings.
- In number theory, he discovered the following theorem on antichains of N. ( An antichain of N, for divisibility, is a set of non nul integers such that no one is divisible by another. It is not difficult to prove that the maximal cardinality of an antichain of E2n = {1,2,...,2n} is n).
[edit] Abouabdillah's Theorem
Let c∈E2n , c = 2kc', c' odd. Then E2n contains an antichain of cardinality n containing c if and only if 2n < 3k+1c'.
This result constitutes a complete solution of a problem the mathematician Paul Erdős posed in 1937 in Amer. Math. Monthly 44 (1937), p.179.
[edit] Publications
[1] - Topologies Linéaires Minimales Sur Un Groupe Abélien. Lecture Notes in Mathematics .1006. (Springer-Verlag). Abelian group Theory. Proceedings Honolulu 1982-83.pp 582-588.
[2] - Topologies de corps A-linéaires . Pacific journal of Mathématics. Vol.107,No.2,1983.
[3] - Sur les similitudes d'un espace euclidien, Revue de Mathématiques Spéciales (RMS) No. 7 Mars 1991.(Vuibert).
[4] - Sur les sous-groupes maximaux du groupe des isométries positives. Revue de Mathématiques de l'enseignement supérieur (RMS) Numéro 9-10. Mai-Juin 1999.(Vuibert).
[5] - Contributions en Géométrie. Monographie de cinq articles de recherche en Géométrie. Avril 2001, ISBN 9954-8096-0-0, Avril 2001.
[6] - Notions fondamentales de géométrie ; Ouvrage destiné à la préparation de l'Agrégation mathématique ; ISBN 9981-1697-2-2, Editions Dar Es-Salam ,1997.
[7] - K. Benabdallah and D. Bouabdillah. Straight and Strongly Straight Primary Modules over Principal Ideal Domains. Abelien Groups and Modules. Proceeding of The Udine Conference . April 1984.CISM Courses And Lectures No.287 Springer Verlag pp.115-130.
[8] - D. Abouabdillah & J.Turgeon, On a 1937 problem of Paul Erdös concerning certain finite sequences of integers none divisible by another. Congressus Numerantium. A conference journal on numerical themes. Vol.43, December,1984, (Winnipeg, Canada), pp.19-22.
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