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'''Driss Abouabdillah''' (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]].

== Contributions ==

*In [[geometry]], he gave several characterizations of similarities as [[mappings]] that preserve [[circles]] or [[spheres]] [http://www.geocities.com/bwakeel/].
*He proposed an alternative [[axiomatic]] approach to [[Euclidean geometry]] by giving an axiomatic definition of [[equipollence]]. [http://www.geocities.com/bwakeel/]
*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 <math>E_{2n}</math> = {1,2,...,2n} is n).

==Abouabdillah's Theorem==
Let c∈<math>E_{2n}</math> , c = 2<sup>k</sup>c', c' odd. Then <math>E_{2n}</math> contains an antichain of cardinality n containing c if and only if 2n < 3<sup>k+1</sup>c'.

This result constitutes a complete solution withof a problem ofthe mathematician [[Paul Erdős]] posed in 1937 in ''Amer. Math. Monthly'' 44 (1937), p.179.

== 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.

(contracted; show full)

[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.

[[Category:Moroccan mathematicians]]
[[Category:1948 births]]
[[Category:Living people]]

[[fr:Driss Abouabdillah]]