, Volume 61, Issue 3-4, pp 365-380

Congruence modularity implies cyclic terms for finite algebras

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Abstract

An n-ary operation f : A n A is called cyclic if it is idempotent and ${f(a_1, a_2, a_3, \ldots , a_n) = f(a_2, a_3, \ldots , a_n, a_1)}$ for every ${a_1, \ldots, a_n \in A}$ . 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 |A|.

Presented by E. Kiss.
The first author was supported by the Grant Agency of the Czech Republic under grant no. 201/06/0664 and by the project of Ministry of Education under grant no. MSM 0021620839. The second and fifth authors were supported by the Eduard Čech Center grant LC505. The third author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant nos. T 48809 and K 60148. The fourth author was supported by the US National Science Foundation, grant no. DMS 0604065.