Algebras with transitive automorphism groups
type: Item
instance of: scholarly article
title: Algebras with transitive automorphism groups
zbMATH Open document ID: 0812.08003
DOI: 10.1007/BF01236508
author: V. Pereyra
published in: Algebra Universalis
publication date: 1994-10-12T00:00:00Z
review text: The author deals with finite simple algebras with transitive automorphism groups. He proves that either the algebra is functionally complete, or it is term-equivalent to one of some specific affine algebras, or it admits a compatible binary central relation. In a subsequent paper [``On simple surjective algebras'', Acta Sci. Math. 59, No. 1-2, 17-23 (1994)] the author has ruled out the last case. In the present paper functional completeness is proved in the presence of certain operations: a nontrivial semiprojection, a majority function, or a nontrivial conservative operation.
reviewed by: Péter P. Pálfy
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 08A35
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 638599
zbMATH Keywords: compatible relation
zbMATH Keywords: finite simple algebras
zbMATH Keywords: transitive automorphism groups
zbMATH Keywords: affine algebras
zbMATH Keywords: functional completeness
MaRDI profile type: Publication
cites work: Plain para primal algebras
cites work: Homogeneous algebras are functionally complete
cites work: Q4278356
cites work: Q3480114
cites work: The primal algebra characterization theorem revisited
cites work: Q5512231
full work available at URL: https://doi.org/10.1007/bf01236508
OpenAlex ID: W2110307492
description: scientific article; zbMATH DE number 638599