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

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*Laszlo Szabo*

**Address.** Bolyai Institute, Aradi vertanuk tere 1, 6720 Szeged, HUNGARY
**E-mail:** szabol@math.u-szeged.hu

**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