{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:22:02Z","timestamp":1773249722603,"version":"3.50.1"},"reference-count":34,"publisher":"Wiley","license":[{"start":{"date-parts":[[2011,8,1]],"date-time":"2011-08-01T00:00:00Z","timestamp":1312156800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A loop is (right) automorphic if all its (right) inner mappings are automorphisms. Using the classification of primitive groups of small degrees, we show that there is no non-associative simple commutative automorphic loop of order less than 2<jats:sup>12<\/jats:sup>, and no non-associative simple automorphic loop of order less than 2500. We obtain numerous examples of non-associative simple right automorphic loops. We also prove that every automorphic loop has the antiautomorphic inverse property, and that a right automorphic loop is automorphic if and only if its conjugations are automorphisms.<\/jats:p>","DOI":"10.1112\/s1461157010000173","type":"journal-article","created":{"date-parts":[[2011,8,30]],"date-time":"2011-08-30T10:34:23Z","timestamp":1314700463000},"page":"200-213","source":"Crossref","is-referenced-by-count":7,"title":["Searching for small simple automorphic loops"],"prefix":"10.1112","volume":"14","author":[{"given":"Kenneth W.","family":"Johnson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael K.","family":"Kinyon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G\u00e1bor P.","family":"Nagy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Petr","family":"Vojt\u011bchovsk\u00fd","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,8,1]]},"reference":[{"key":"S1461157010000173_ref23","first-page":"195","article-title":"Connected transversals to nilpotent groups","volume":"2","author":"Mazur","year":"2007","journal-title":"J. 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P. and Vojt\u011bchovsk\u00fd P. , \u2018Loops: computing with quasigroups and loops in GAP, version 2.1.0\u2019, available at http:\/\/www.math.du.edu\/loops."},{"key":"S1461157010000173_ref4","first-page":"117","article-title":"Self-invariant 1-factorizations of complete graphs and finite Bol loops of exponent 2","volume":"51","author":"Baumeister","year":"2010","journal-title":"Beitr\u00e4ge Algebra Geom."},{"key":"S1461157010000173_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2016-7"},{"key":"S1461157010000173_ref6","doi-asserted-by":"publisher","DOI":"10.2307\/1969612"},{"key":"S1461157010000173_ref14","unstructured":"[14] The GAP group, GAP\u2014groups, algorithms, and programming, version 4.4.12, 2008, available athttp:\/\/www.gap-system.org."},{"key":"S1461157010000173_ref18","doi-asserted-by":"publisher","DOI":"10.1080\/00927870903200877"},{"key":"S1461157010000173_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2009.05.001"},{"key":"S1461157010000173_ref9","unstructured":"[9] Dr\u00e1pal A. , Latin squares and groups, MS Thesis, Charles University, Prague, 1979."},{"key":"S1461157010000173_ref31","unstructured":"[31] Soicher L. 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