**Beiträge zur Algebra und Geometrie
**

Contributions to Algebra and Geometry

Vol. 39, No. 1, pp. 181-204 (1998)

#
Clones Closed with Respect to Permutation Groups or Transformation Semigroups

##
V. V. Gorlov; R. Pöschel

Dept. of Mathematics, Byelorussian State University

pr-t F. Skoriny 4, 220050 Minsk, Belarus

e-mail: valera@gorlov.belpak.minsk.by
Technische Universität Dresden, Institut für Algebra

01062 Dresden, Germany

e-Mail: poeschel@math.tu-dresden.de

**Abstract:** This paper presents a new approach to the classification of finite algebras with respect to actions of permutation groups or transformation semigroups on the clone of term operations. In particular it is a contribution to the structural investigation of the (uncountable) lattice ${\cal L}_A$ of clones on a finite set $A$, which can be divided into (sometimes finitely many) intervals represented by so-called $G$-clones. A Galois theory for $G$-clones is developed. Concrete results are presented for clones - and, more generally, for closed classes - on base sets $A$ with two or three elements.

**Keywords:** finite algebras; permutation groups; clone; Galois theory

**Classification (MSC91):** 20B25; 08A40

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]