{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,11,17]],"date-time":"2022-11-17T06:50:03Z","timestamp":1668667803713},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,11]]},"abstract":"<jats:p> Let G be a finite group and \u03c0(G) = {p<jats:sub>1<\/jats:sub>, p<jats:sub>2<\/jats:sub>,\u2026,p<jats:sub>k<\/jats:sub>}. For p \u2208 \u03c0(G), we put deg (p) := |{q \u2208 \u03c0(G)|p ~ q}|, which is called the degree of p. We also define D(G) := ( deg (p<jats:sub>1<\/jats:sub>), deg (p<jats:sub>2<\/jats:sub>), \u2026, deg (p<jats:sub>k<\/jats:sub>)), where p<jats:sub>1<\/jats:sub> &lt; p<jats:sub>2<\/jats:sub> &lt; \u22ef &lt; p<jats:sub>k<\/jats:sub>, which is called the degree pattern of G. Using the classification of finite simple groups, we characterize the projective general linear group PGL(2,q)(q a prime power) by its order and degree pattern in the present paper. <\/jats:p>","DOI":"10.1142\/s0218196709005433","type":"journal-article","created":{"date-parts":[[2009,12,16]],"date-time":"2009-12-16T06:22:12Z","timestamp":1260944532000},"page":"873-889","source":"Crossref","is-referenced-by-count":9,"title":["CHARACTERIZATION OF THE PROJECTIVE GENERAL LINEAR GROUPS PGL(2,q) BY THEIR ORDERS AND DEGREE PATTERNS"],"prefix":"10.1142","volume":"19","author":[{"given":"LIANGCAI","family":"ZHANG","sequence":"first","affiliation":[{"name":"College of Mathematics and Physics, Chongqing University, Shapingba, Chongqing 400044, China"}]},{"given":"XUEFENG","family":"LIU","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","first-page":"485","volume":"20","author":"Chen G. Y.","journal-title":"J. Southwest China Normal University"},{"key":"rf3","first-page":"184","volume":"185","author":"Chen G. Y.","journal-title":"J. Algebra"},{"key":"rf4","volume-title":"Atlas of Finite Groups","author":"Conway J. H.","year":"1985"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(75)90083-3"},{"key":"rf6","volume-title":"Finite Groups","author":"Gorenstein D.","year":"1980"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1993.1048"},{"key":"rf9","first-page":"787","volume":"180","author":"Kondratev A. S.","journal-title":"Math. Sb."},{"key":"rf11","first-page":"463","volume":"47","author":"Moghaddamfar A. R.","journal-title":"Beitrage zur Algebra und Geometrie"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1142\/S1005386708000424"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1142\/S1005386705000398"},{"key":"rf16","first-page":"373","volume":"7","author":"Lucido M. S.","journal-title":"J. Group Theory"},{"key":"rf17","volume-title":"Permutation Groups","author":"Passman D.","year":"1968"},{"key":"rf18","volume-title":"Group Tables","author":"Thomas A. D.","year":"1980"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01162958"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(81)90218-0"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1007\/s11464-008-0026-9"},{"key":"rf22","first-page":"191","volume":"44","author":"Zhang L. C.","journal-title":"Archivum Mathematicum (BRNO) Tomus"},{"key":"rf23","first-page":"275","volume":"6","author":"Zhang L. C.","journal-title":"Algebra Colloquium"},{"key":"rf26","first-page":"120","volume":"34","author":"Zhang L. C.","journal-title":"J. Guangxi University (Natural Science Edition)"},{"key":"rf27","first-page":"7","volume":"24","author":"Zhang L. C.","journal-title":"J. Suzhou University (Natural Science Edition)"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196709005433","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:46:51Z","timestamp":1565171211000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196709005433"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11]]},"references-count":20,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,11]]}},"alternative-id":["10.1142\/S0218196709005433"],"URL":"https:\/\/doi.org\/10.1142\/s0218196709005433","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11]]}}}