Abstract
Let A be a finite algebra in a congruence permutable variety. We assume that for every subdirectly irreducible homomorphic image of A the centralizer of the monolith is n-supernilpotent. Then the clone of polynomial functions on A is determined by relations of arity |A|n+1. As consequences we obtain finite implicit descriptions of the polynomial functions on finite local rings with 1 and on finite groups G such that in every subdirectly irreducible quotient of G the centralizer of the monolith is a p-group.
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Presented by Á. Szendrei.
The author acknowledges support from the Austrian Science Fund (Erwin-Schrödinger-Grant J2637-N18), the University of Colorado at Boulder and from the Portuguese Project ISFL-1-143 of CAUL financed by FCT and FEDER.
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Mayr, P. Mal’cev algebras with supernilpotent centralizers. Algebra Univers. 65, 193–211 (2011). https://doi.org/10.1007/s00012-011-0124-5
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DOI: https://doi.org/10.1007/s00012-011-0124-5