{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T22:40:49Z","timestamp":1768776049961,"version":"3.49.0"},"reference-count":17,"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>Suppose that <jats:italic>p<\/jats:italic> is 3, 5 or 7. In this paper, faithful permutation representations of maximal <jats:italic>p<\/jats:italic>-local subgroups are constructed, and the radical <jats:italic>p<\/jats:italic>-chains of the Baby Monster B are classified. Hence, the Alperin weight conjecture and the Uno reductive conjecture can be verified for B, the latter being a refinement of Dade's reductive conjecture and the Isaacs-Navarro conjecture.<\/jats:p>","DOI":"10.1112\/s1461157000001078","type":"journal-article","created":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T07:42:22Z","timestamp":1375774942000},"page":"120-166","source":"Crossref","is-referenced-by-count":8,"title":["The Alperin Weight Conjecture and Uno's Conjecture for the Baby Monster B, <sub>p<\/sub> Odd"],"prefix":"10.1112","volume":"7","author":[{"given":"Jianbei","family":"An","sequence":"first","affiliation":[]},{"given":"R. A.","family":"Wilson","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,2,1]]},"reference":[{"key":"S1461157000001078_ref005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196799000369"},{"key":"S1461157000001078_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/047.1\/933373"},{"key":"S1461157000001078_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF01232023"},{"key":"S1461157000001078_ref009","first-page":"45","article-title":"Counting characters in blocksCounting characters in blocks","author":"Dade","year":"1997","journal-title":"II.9, Representation theory of finite groups (Columbus, OH, 1995), Ohio State Univ. Math. Res. Inst. Publ."},{"key":"S1461157000001078_ref004","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1997.7410"},{"key":"S1461157000001078_ref006","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"S1461157000001078_ref002","doi-asserted-by":"publisher","DOI":"10.1515\/jgth.2000.029"},{"key":"S1461157000001078_ref007","volume-title":"Atlas of finite groups","author":"Conway","year":"1985"},{"key":"S1461157000001078_ref015","article-title":"Conjectures on character degrees for the simple Thompson group","author":"Uno","journal-title":"Osaka J. Math."},{"key":"S1461157000001078_ref010","unstructured":"10. The GAP Team, \u2018GAP - Groups, Algorithms, and Programming\u2019, Version 4. Lehrstuhl D f\u00fcr Mathematik, RWTH Aachen, and School of Mathematical and Computational Sciences, University of St Andrews (2000)."},{"key":"S1461157000001078_ref011","unstructured":"11. G.Hiss , Lux K. , Brauer trees of sporadic groups (Oxford Science Publications, 1989)."},{"key":"S1461157000001078_ref013","doi-asserted-by":"publisher","DOI":"10.2307\/1971234"},{"key":"S1461157000001078_ref012","doi-asserted-by":"publisher","DOI":"10.2307\/3597192"},{"key":"S1461157000001078_ref014","first-page":"307","article-title":"Computer construction of the Monsters","volume":"1","author":"Linton","year":"1998","journal-title":"J. Group Theory"},{"key":"S1461157000001078_ref003","unstructured":"3. An Jianbei , Eaton C. W. , \u2018Modular representation theory of blocks with trivial intersection defect groups\u2019, Algebr. Represent. Theory, to appear."},{"key":"S1461157000001078_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/BF01404677"},{"key":"S1461157000001078_ref017","unstructured":"17. Wilson R. A. , \u2018ATLAS of finite group representations\u2019, http:\/\/www.mat.bham.ac.uk\/atlas."}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157000001078","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T20:46:55Z","timestamp":1559854015000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157000001078\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004]]},"references-count":17,"alternative-id":["S1461157000001078"],"URL":"https:\/\/doi.org\/10.1112\/s1461157000001078","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004]]}}}