Infinite algebras with 3-transitive groups of weak automorphisms

László Szabó

Archivum Mathematicum (2001)

  • Volume: 037, Issue: 4, page 245-256
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Szabó, László. "Infinite algebras with 3-transitive groups of weak automorphisms." Archivum Mathematicum 037.4 (2001): 245-256. <http://eudml.org/doc/248731>.

@article{Szabó2001,
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.},
author = {Szabó, László},
journal = {Archivum Mathematicum},
keywords = {locally functionally complete algebra; weak automorphism; locally functionally complete algebra; weak automorphism},
language = {eng},
number = {4},
pages = {245-256},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Infinite algebras with 3-transitive groups of weak automorphisms},
url = {http://eudml.org/doc/248731},
volume = {037},
year = {2001},
}

TY - JOUR
AU - Szabó, László
TI - Infinite algebras with 3-transitive groups of weak automorphisms
JO - Archivum Mathematicum
PY - 2001
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 037
IS - 4
SP - 245
EP - 256
AB - 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.
LA - eng
KW - locally functionally complete algebra; weak automorphism; locally functionally complete algebra; weak automorphism
UR - http://eudml.org/doc/248731
ER -

References

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  16. 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. MR1342550
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