{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T07:17:29Z","timestamp":1771485449776,"version":"3.50.1"},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2013,9,30]],"date-time":"2013-09-30T00:00:00Z","timestamp":1380499200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Aust. Math. Soc."],"published-print":{"date-parts":[[2014,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We address the question of the dualizability of nilpotent Mal\u2019cev algebras, showing that nilpotent finite Mal\u2019cev algebras with a nonabelian supernilpotent congruence are inherently nondualizable. In particular, finite nilpotent nonabelian Mal\u2019cev algebras of finite type are nondualizable if they are direct products of algebras of prime power order. We show that these results cannot be generalized to nilpotent algebras by giving an example of a group expansion of infinite type that is nilpotent and nonabelian, but dualizable. To our knowledge this is the first construction of a nonabelian nilpotent dualizable algebra. It has the curious property that all its nonabelian finitary reducts with group operation are nondualizable. We were able to prove dualizability by utilizing a new clone theoretic approach developed by Davey, Pitkethly, and Willard. Our results suggest that supernilpotence plays an important role in characterizing dualizability among Mal\u2019cev algebras.<\/jats:p>","DOI":"10.1017\/s1446788713000517","type":"journal-article","created":{"date-parts":[[2013,9,30]],"date-time":"2013-09-30T10:45:23Z","timestamp":1380537923000},"page":"1-24","source":"Crossref","is-referenced-by-count":7,"title":["SUPERNILPOTENCE PREVENTS DUALIZABILITY"],"prefix":"10.1017","volume":"96","author":[{"given":"WOLFRAM","family":"BENTZ","sequence":"first","affiliation":[]},{"given":"PETER","family":"MAYR","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2013,9,30]]},"reference":[{"key":"S1446788713000517_r18","first-page":"69","volume-title":"Dualities, Interpretability and Ordered Structures","author":"Willard","year":"1999"},{"key":"S1446788713000517_r13","unstructured":"M. H. Nickodemus , \u2018Natural dualities for finite groups with abelian Sylow subgroups\u2019. ProQuest LLC, Ann Arbor, MI, 2007, PhD Thesis, University of Colorado at Boulder."},{"key":"S1446788713000517_r6","doi-asserted-by":"publisher","DOI":"10.1007\/PL00000344"},{"key":"S1446788713000517_r19","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700014301"},{"key":"S1446788713000517_r4","volume-title":"Natural Dualities for the Working Algebraist","author":"Clark","year":"1998"},{"key":"S1446788713000517_r10","doi-asserted-by":"publisher","DOI":"10.1007\/s000120050132"},{"key":"S1446788713000517_r9","volume-title":"Commutator Theory for Congruence Modular Varieties","author":"Freese","year":"1987"},{"key":"S1446788713000517_r17","unstructured":"R. Willard , \u2018Four unsolved problems in congruence permutable varieties\u2019, Talk at the Conference on Order, Algebra, and Logics, Nashville, 2007."},{"key":"S1446788713000517_r2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1946-0017288-3"},{"key":"S1446788713000517_r12","volume-title":"Algebras, Lattices, Varieties, Vol. I","author":"McKenzie","year":"1987"},{"key":"S1446788713000517_r16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01258048"},{"key":"S1446788713000517_r11","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-011-0124-5"},{"key":"S1446788713000517_r1","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-010-0084-1"},{"key":"S1446788713000517_r3","first-page":"41","volume-title":"Proc. Dresden Conference 2000 (AAA 60) and the Summer School 1999","author":"Bulatov","year":"2001"},{"key":"S1446788713000517_r5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196703001444"},{"key":"S1446788713000517_r7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190710"},{"key":"S1446788713000517_r8","doi-asserted-by":"publisher","DOI":"10.1142\/S021819671100673X"},{"key":"S1446788713000517_r14","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700003827"},{"key":"S1446788713000517_r15","doi-asserted-by":"publisher","DOI":"10.1007\/s000120050004"}],"container-title":["Journal of the Australian Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1446788713000517","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T00:04:25Z","timestamp":1555977865000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1446788713000517\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,30]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,2]]}},"alternative-id":["S1446788713000517"],"URL":"https:\/\/doi.org\/10.1017\/s1446788713000517","relation":{},"ISSN":["1446-7887","1446-8107"],"issn-type":[{"value":"1446-7887","type":"print"},{"value":"1446-8107","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9,30]]}}}