{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T06:51:23Z","timestamp":1772434283783,"version":"3.50.1"},"reference-count":24,"publisher":"Wiley","license":[{"start":{"date-parts":[[2010,2,1]],"date-time":"2010-02-01T00:00:00Z","timestamp":1264982400000},"content-version":"unspecified","delay-in-days":2223,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2004]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Prior to this paper, all small simple groups were known to be efficient, but the status of four of their covering groups was unknown. Nice, efficient presentations are provided in this paper for all of these groups, resolving the previously unknown cases. The authors\u2018presentations are better than those that were previously available, in terms of both length and computational properties. In many cases, these presentations have minimal possible length. The results presented here are based on major amounts of computation. Substantial use is made of systems for computational group theory and, in partic-ular, of computer implementations of coset enumeration. To assist in reducing the number of relators, theorems are provided to enable the amalgamation of power relations in certain presentations. The paper concludes with a selection of unsolved problems about efficient presentations for simple groups and their covers.<\/jats:p>","DOI":"10.1112\/s1461157000001121","type":"journal-article","created":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T11:42:22Z","timestamp":1375789342000},"page":"266-283","source":"Crossref","is-referenced-by-count":7,"title":["Nice Efficient Presentions for all Small Simple Groups and their Covers"],"prefix":"10.1112","volume":"7","author":[{"given":"Colin M.","family":"Campbell","sequence":"first","affiliation":[]},{"given":"George","family":"Havas","sequence":"additional","affiliation":[]},{"given":"Colin","family":"Ramsay","sequence":"additional","affiliation":[]},{"given":"Edmund F.","family":"Robertson","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,2,1]]},"reference":[{"key":"S1461157000001121_ref010","volume-title":"Atlas of finite groups","author":"Conway","year":"1985"},{"key":"S1461157000001121_ref005","doi-asserted-by":"publisher","DOI":"10.1080\/00927878208822711"},{"key":"S1461157000001121_ref019","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-120027920"},{"key":"S1461157000001121_ref017","doi-asserted-by":"crossref","unstructured":"17. Havas George and Ramsay Colin , Coset enumeration: ACE version 3.001, (2001); http:\/\/www.itee.uq.edu.au\/~havas\/ace3001.tar.gz.","DOI":"10.1515\/9783110872743.183"},{"key":"S1461157000001121_ref018","first-page":"238","volume-title":"Short balanced presentations of perfect groups","author":"Havas","year":"2003"},{"key":"S1461157000001121_ref016","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700018529"},{"key":"S1461157000001121_ref013","unstructured":"13. Gamble Greg , Hulpke Alexander , Havas George and Ramsay Colin , G AP package ACE; Advanced Coset Enumerator, (2004); http:\/\/www.gap-system.org\/Packages\/ace.html."},{"key":"S1461157000001121_ref012","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700030068"},{"key":"S1461157000001121_ref020","doi-asserted-by":"publisher","DOI":"10.1080\/00927878608823336"},{"key":"S1461157000001121_ref023","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1972-118-x"},{"key":"S1461157000001121_ref009","doi-asserted-by":"publisher","DOI":"10.1080\/00927877908822409"},{"key":"S1461157000001121_ref015","unstructured":"15. THE GAP GROUP, Balanced presentations for covering groups of simple groups, (2004); http:\/\/www.gap-system.org\/Doc\/Examples\/balanced.html."},{"key":"S1461157000001121_ref024","first-page":"137","volume-title":"The Schur multiplier: an elementary approach","author":"Wiegold","year":"1982"},{"key":"S1461157000001121_ref008","first-page":"65","volume-title":"Efficient presentations for finite simple groups and related groups","author":"Cambpell","year":"1989"},{"key":"S1461157000001121_ref021","unstructured":"21. The New York Group Theory Cooperative, Magnus; http:\/\/www.grouptheory.org\/."},{"key":"S1461157000001121_ref001","first-page":"331","article-title":"\u2018The unsolvability of efficiency for groups\u2019","volume":"22","author":"Ahmad","year":"1998","journal-title":"Southeast Asian Math. Bull."},{"key":"S1461157000001121_ref014","unstructured":"14. THE GAP GROUP, GAP - Groups, algorithms, and programming, Version 4.3, (2000;) http:\/\/www.gap-system.org\/."},{"key":"S1461157000001121_ref011","first-page":"73","article-title":"\u2018The abstract groups Gmnp\u2018","volume":"45","author":"Coxeter","year":"1939","journal-title":"Trans. Amer. Math. 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