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Infinite algebras with 3-transitive groups of weak automorphisms
Archivum mathematicum, Tome 37 (2001) no. 4, pp. 245-256 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 08A05, 08A35, 08A40
Keywords: locally functionally complete algebra; weak automorphism 
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Szabó, László. Infinite algebras with 3-transitive groups of weak automorphisms. Archivum mathematicum, Tome 37 (2001) no. 4, pp. 245-256. http://geodesic.mathdoc.fr/item/ARM_2001_37_4_a0/

[1] Csákány, B.: Homogeneous algebras are functionally complete. Algebra Universalis 11 (1980), 149–158. | MR

[2] Fried, E., Szabó, L. and Szendrei, Á.: Algebras with $p$-uniform principal congruences. Studia Sci. Math. Hungar. 16 (1981), 229–235. | MR

[3] Goetz, A.: On weak isomorphisms and weak homomorphisms of abstract algebras. Colloq. Math. 14 (1966), 163–167. | MR | Zbl

[4] Kaiser, H. K. and Márki, L.: Remarks on a paper of L. Szabó and Szendrei, Á. Acta Sci. Math. (Szeged) 42 (1980), 95–98. | MR

[5] E. Marczewski, E.: Independence in abstract algebras. Colloq. Math. 14 (1966), 169–188. | MR

[6] Pálfy, P. P., Szabó, L. and Szendrei, Á.: Algebras with doubly transitive automorphism groups. in: Finite Algebra and Multiple-Valued Logic (Proc. Conf. Szeged, 1979), Colloq. Math. Soc. J. Bolyai, vol. 28, North-Holland, Amsterdam, 1981; 521–535. | MR

[7] Pálfy, P. P., Szabó, L. and Szendrei, Á.: Automorphism groups and functional completeness. Algebra Universalis 15 (1982), 385–400. | MR

[8] Rosenberg, I. G., and Szabó, L.: Local completeness I. Algebra Universalis 18 (1984), 308–326. | MR

[9] Salomaa, A.: A theorem concerning the composition of functions of several variables ranging over a finite set. J. Symbolic Logic 25 (1960), 203–208. | MR

[10] Szabó, L. and Szendrei, Á.: Almost all algebras with triply transitive automorphism groups are functionally complete. Acta Sci. Math. (Szeged) 41 (1979), 391–402. | MR

[11] Szabó, L.: Interpolation in algebras with doubly primitive automorphism groups. Elektron. Informationsverarbeit. Kybernetik 19 (1983), 603–610. | MR

[12] Szabó, L.: Basic permutation groups on infinite sets. Acta Sci. Math. (Szeged) 47 (1984), 61–70. | MR

[13] Szabó, L.: Triply transitive algebras. Acta Sci. Math. (Szeged) 51 (1987), 221–227. | MR

[14] Szabó, L.: Algebras with transitive automorphism groups. Algebra Universalis 31 (1994), 589–598. | MR

[15] Szabó, L.: On simple surjective algebras. Acta Sci. Math. (Szeged) 59 (1994), 17–23. | MR

[16] Szabó, L.: Simple, surjective, transitive algebras. in: General Algebra and Ordered Sets (Proc. of the Summer School, 1994), Dept. of Algebra and Geometry, Palacký University Olomouc, Olomouc, Czech Republic; 138-143. | MR

[17] Szabó, L.: Characteristically simple algebras. Acta Sci. Math. (Szeged) 63 (1997), 51–70. | MR

[18] Szabó, L.: Algebras that are simple with weak automorphisms. Algebra Universalis 42 (1999), 205–233. | MR

[19] Wielandt, H.: Finite permutation group. Academic Press, New York and London, 1964. | MR