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On algebras with many symmetric operations.

Carvalho, C. and Krokhin, A. (2016) 'On algebras with many symmetric operations.', International journal of algebra and computation., 26 (05). pp. 1019-1032.


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.

Item Type:Article
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Publisher 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
Date accepted:03 June 2016
Date deposited:19 July 2016
Date of first online publication:19 July 2016
Date first made open access:19 July 2017

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