"Mal'cev algebras with supernilpotent centralizers"
, in Algebra Universalis, Vol. 65, Springer Basel AG 2011, Seite(n) 193-211, 2011, ISSN: 0002-5240
Mal'cev algebras with supernilpotent centralizers
Sprache des Titels:
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.