{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T11:24:47Z","timestamp":1758281087009},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2012,11]]},"abstract":"<jats:p> Given tuples a<jats:sub>1<\/jats:sub>, \u2026, a<jats:sub>k<\/jats:sub> and b in A<jats:sup>n<\/jats:sup> for some algebraic structure A, the subpower membership problem asks whether b is in the subalgebra of A<jats:sup>n<\/jats:sup> that is generated by a<jats:sub>1<\/jats:sub>, \u2026, a<jats:sub>k<\/jats:sub>. For A a finite group, there is a folklore algorithm which decides this problem in time polynomial in n and k. We show that the subpower membership problem for any finite Mal'cev algebra is in NP and give a polynomial time algorithm for any finite Mal'cev algebra with finite signature and prime power size that has a nilpotent reduct. In particular, this yields a polynomial algorithm for finite rings, vector spaces, algebras over fields, Lie rings and for nilpotent loops of prime power order. <\/jats:p>","DOI":"10.1142\/s0218196712500750","type":"journal-article","created":{"date-parts":[[2012,9,24]],"date-time":"2012-09-24T05:20:34Z","timestamp":1348464034000},"page":"1250075","source":"Crossref","is-referenced-by-count":10,"title":["THE SUBPOWER MEMBERSHIP PROBLEM FOR MAL'CEV ALGEBRAS"],"prefix":"10.1142","volume":"22","author":[{"given":"PETER","family":"MAYR","sequence":"first","affiliation":[{"name":"CAUL, Centro de \u00c1lgebra da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2012,12,3]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2010-10395-7"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01187059"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1137\/050628957"},{"key":"rf4","series-title":"With Applications to Finite Groups and Orders","volume-title":"Methods of Representation Theory","author":"Curtis C. W.","year":"1981"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2009.03.042"},{"key":"rf6","volume-title":"Commutator Theory for Congruence Modular Varieties, London Mathematical Society Lecture Note Series","volume":"125","author":"Freese R.","year":"1987"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/076"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.06.057"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-011-0124-5"},{"key":"rf11","volume-title":"Algebras, Lattices, Varieties","author":"McKenzie R. N.","year":"1987"},{"key":"rf12","series-title":"Annals of Mathematics Studies","volume-title":"The Two-Valued Iterative Systems of Mathematical Logic","volume":"5","author":"Post E. L.","year":"1941"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196712500750","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T08:32:12Z","timestamp":1565166732000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196712500750"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11]]},"references-count":11,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2012,12,3]]},"published-print":{"date-parts":[[2012,11]]}},"alternative-id":["10.1142\/S0218196712500750"],"URL":"https:\/\/doi.org\/10.1142\/s0218196712500750","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,11]]}}}