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On algebras with many symmetric operations

Carvalho, C.; Krokhin, A.

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Authors

C. Carvalho



Abstract

An n-ary operation f is called symmetric if, for all permutations π of {1, . . . , n}, it satisfies the identity f(x1, x2, . . . , xn) = f(xπ(1), xπ(2), . . . , xπ(n) ). We show that, for each finite algebra A, either it has symmetric term operations of all arities or else some finite algebra in the variety generated by A has two automorphisms without a common fixed point. We also show this two-automorphism condition cannot be replaced by a single fixed-point-free automorphism.

Citation

Carvalho, C., & Krokhin, A. (2016). On algebras with many symmetric operations. International Journal of Algebra and Computation, 26(05), 1019-1032. https://doi.org/10.1142/s0218196716500429

Journal Article Type Article
Acceptance Date Jun 3, 2016
Online Publication Date Jul 19, 2016
Publication Date Aug 1, 2016
Deposit Date Jul 14, 2016
Publicly Available Date Jul 19, 2017
Journal International Journal of Algebra and Computation
Print ISSN 0218-1967
Electronic ISSN 1793-6500
Publisher World Scientific Publishing
Peer Reviewed Peer Reviewed
Volume 26
Issue 05
Pages 1019-1032
DOI https://doi.org/10.1142/s0218196716500429

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Accepted Journal Article (326 Kb)
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Copyright Statement
Electronic version of an article published as International Journal of Algebra and Computation, August 2016, Vol. 26, No. 05 : pp. 1019-1031, 10.1142/S0218196716500429, © copyright World Scientific Publishing Company





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