Congruence modularity implies cyclic terms for finite algebras

Barto, Libor and Kozik, Marcin and Maróti, Miklós and McKenzie, Ralph and Niven, Todd (2009) Congruence modularity implies cyclic terms for finite algebras. Algebra Universalis, 61 (3-4). pp. 365-380. ISSN 0002-5240

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Abstract

An n-ary operation f : A(n) -> A is called cyclic if it is idempotent and f(a(1), a(2), a(3), ... , a(n)) = f(a(2), a(3), ... , a(n), a(1)) for every a(1), ... , a(n) is an element of A. We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than vertical bar A vertical bar.

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