On algebras with many symmetric operations

Carvalho, C.; Krokhin, A.

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
• Public URL: https://durham-repository.worktribe.com/output/1379605