Infinite algebras with 3-transitive groups of weak automorphisms. (English) Zbl 1069.08001

Summary: 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.


08A35 Automorphisms and endomorphisms of algebraic structures
08A40 Operations and polynomials in algebraic structures, primal algebras
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