{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T23:08:02Z","timestamp":1706224082957},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2005,4]]},"abstract":"<jats:p>The members of the class C<jats:sub>6<\/jats:sub>in Aschbacher's structure theorem for subgroups of the general linear group GL (d,q) are the normalizers of certain absolutely irreducible, symplectic-type r-groups, where r is a prime, d a power of r and q \u2261 1 ( mod r). For a prime r &gt; 2 and d = r, we present a constructive one-sided Monte Carlo algorithm to recognize whether or not a given subgroup G of GL (r,q) contains a normal extra-special r-group of order r<jats:sup>3<\/jats:sup>and exponent r. In the former case the algorithm returns a homomorphism from G into SL (2,r) with kernel being the extra-special r-group times the center.<\/jats:p>","DOI":"10.1142\/s021819670500230x","type":"journal-article","created":{"date-parts":[[2005,5,12]],"date-time":"2005-05-12T11:59:43Z","timestamp":1115899183000},"page":"367-394","source":"Crossref","is-referenced-by-count":2,"title":["CONSTRUCTIVE RECOGNITION OF NORMALIZERS OF SMALL EXTRA-SPECIAL MATRIX GROUPS"],"prefix":"10.1142","volume":"15","author":[{"given":"ALICE C.","family":"NIEMEYER","sequence":"first","affiliation":[{"name":"School of Mathematics &amp; Statistics, University of Western Australia, Nedlands, WA 6009, Australia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01388470"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03338-8"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1080\/00927879508825509"},{"key":"rf6","volume-title":"Linear Groups with an Exposition of the Galois Field Theory","author":"Dickson L. E.","year":"1901"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01272074"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(92)90142-9"},{"key":"rf10","volume-title":"Almost Simple K-groups","author":"Gorenstein D.","year":"1998"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.0286"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-64981-3"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1995.1238"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1142\/9789812564481_0007"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511629235"},{"key":"rf16","doi-asserted-by":"crossref","unstructured":"C. R.\u00a0Leedham-Green, Groups and computation III (Columbus, OH, 1999) (de Gruyter, Berlin, 2001)\u00a0pp. 229\u2013247.","DOI":"10.1515\/9783110872743.229"},{"key":"rf17","volume-title":"An Introduction to the Theory of Numbers","author":"Niven I.","year":"1991"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819670500230X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T22:06:19Z","timestamp":1706220379000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819670500230X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,4]]},"references-count":15,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,4]]}},"alternative-id":["10.1142\/S021819670500230X"],"URL":"https:\/\/doi.org\/10.1142\/s021819670500230x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,4]]}}}