Growth rates of algebras, III: finite solvable algebras

Abstract

We investigate how the behavior of the function d A (n), which gives the size of a least size generating set for A n , influences the structure of a finite solvable algebra A.1991 Mathematics Subject Classification. 08A40 (08A55, 08B05).

Between an $n$-ary and an $n{+}1$-ary near-unanimity term

“…We are not claiming that the problems below are difficult. Edge terms are an important generalization of near-unanimity terms and, possibly in equivalent formulations, play a chief role in many computational problems, e. g. [1,2,5,7,8,15,20,21,22,23] and further references in the quoted papers. An edge term implies congruence modularity; moreover, a congruence distributive variety V has a k-edge term if and only if V has a k-near-unanimity term [7].…”

Growth Rates of Algebras, I: Pointed Cube Terms

“…This extends Wiegold's result (I) for groups to a setting that includes, as special cases, any finite algebra with a Maltsev term (in particular, any finite algebra in a congruence uniform variety) or any finite algebra with a majority term. [20]. We investigate growth rates of finite solvable algebras.…”