Infinite algebras with $3$-transitive groups of weak automorphisms

Laszlo Szabo

Address. Bolyai Institute, Aradi vertanuk tere 1, 6720 Szeged, HUNGARY


Abstract. The infinite algebras with 3-transitive groups of weak automorphisms are investigated. Among others it is shown that if an infinite algebra with 3-transitive group of weak automorphisms has a nontrivial idempotent polynomial operation then either it is locally functionally complete or it is polynomially equivalent to a vector space over the two element field or it is a simple algebra that is semi-affine with respect to an elementary 2-group. In the second and third cases the group of weak automorphisms cannot be 4-transitive.

AMSclassification. 08A40

Keywords. Locally functionally complete algebra, weak automorphism