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

Szabó, László

Arch. Math., Brno 37, No. 4, 245-256 (2001).

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.

MSC:

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

Keywords:

locally functionally complete algebra; weak automorphism