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CLONES CLOSED UNDER CONJUGATION I: CLONES WITH CONSTANTS

KEITH A. KEARNES

Department of Mathematics, University of Colorado, Boulder, CO 80309-0395, USA

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ÁGNES SZENDREI

Department of Mathematics, University of Colorado, Boulder, CO 80309-0395, USA

Bolyai Institute, Aradi vértanúk tere 1, H–6720 Szeged, Hungary

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https://doi.org/10.1142/S0218196708004251Cited by:0 (Source: Crossref)

Abstract

We show that if G ≤ S_A is a permutation group on a finite set A satisfying |A| ≥ 3, then the set of G-closed clones on A that contain all constant operations is finite iff G = S_A, A_A, AGL(1,5) (|A| = 5), PSL(2,5) (|A| = 6), PGL(2,5) (|A| = 6), PGL(2,7) (|A| = 8), PGL(2,8) (|A| = 9), or PΓL(2,8) (|A| = 9).

Keywords:

AMSC: Primary 08A05, Secondary 08A40, Secondary 08A35, Secondary 03B50

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