{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T08:07:56Z","timestamp":1773216476564,"version":"3.50.1"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,6]]},"abstract":"<jats:p> We prove that, on a set of size n, the number of clones that contain a group operation and all constant functions is finite if n is squarefree. This confirms a conjecture by Pawe\u0142 Idziak from [5] where the converse implication was shown. Our result follows from the observation that the polynomial clone of an expansion of a squarefree group is uniquely determined by its binary functions. We also note that, in general, such a clone is not determined by the congruence lattice and the commutator operation of the corresponding algebra. This refutes a second conjecture from [5]. <\/jats:p>","DOI":"10.1142\/s0218196708004597","type":"journal-article","created":{"date-parts":[[2008,6,24]],"date-time":"2008-06-24T05:38:40Z","timestamp":1214285920000},"page":"759-777","source":"Crossref","is-referenced-by-count":7,"title":["POLYNOMIAL CLONES ON SQUAREFREE GROUPS"],"prefix":"10.1142","volume":"18","author":[{"given":"PETER","family":"MAYR","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Algebra, Johannes Kepler Universit\u00e4t Linz, 4040 Linz, Austria"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/s10474-006-0530-x"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1080\/10236620215291"},{"key":"rf3","volume-title":"Methods of Representation Theory","author":"Curtis C. W.","year":"1981"},{"key":"rf4","unstructured":"J.\u00a0Hagemann and C.\u00a0Herrmann, Universal Algebra, Esztergom (Hungary)\u00a029 (Colloq. Math. Soc. J\u00e1nos Bolyai, 1982)\u00a0pp. 345\u2013360."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S021819679900014X"},{"key":"rf6","series-title":"Berichte der mathematischen Institute","volume":"563","author":"Mayr P.","year":"2007"},{"key":"rf7","first-page":"37","volume":"72","author":"Mayr P.","journal-title":"Acta Sci. Math. (Szeged)"},{"key":"rf8","volume-title":"Algebras, Lattices, Varieties","author":"McKenzie R. N.","year":"1987"},{"key":"rf9","volume-title":"Near-Rings","author":"Pilz G. F.","year":"1983"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8594-1"},{"key":"rf11","volume-title":"Ring Theory","author":"Rowen L. H.","year":"1988"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196708004597","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:43:17Z","timestamp":1565170997000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196708004597"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6]]},"references-count":11,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,6]]}},"alternative-id":["10.1142\/S0218196708004597"],"URL":"https:\/\/doi.org\/10.1142\/s0218196708004597","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,6]]}}}