{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:54:33Z","timestamp":1753883673918,"version":"3.41.2"},"reference-count":13,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,8,23]],"date-time":"2011-08-23T00:00:00Z","timestamp":1314057600000},"content-version":"vor","delay-in-days":234,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>Let <jats:italic>G<\/jats:italic> be a permutation group of degree <jats:italic>n<\/jats:italic> viewed as a subgroup of the symmetric\ngroup <jats:italic>S<\/jats:italic>\u2245<jats:italic>S<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>. We show that if the irreducible character of <jats:italic>S<\/jats:italic> corresponding to the partition of <jats:italic>n<\/jats:italic> into subsets of sizes <jats:italic>n<\/jats:italic> \u2212 2 and 2, that is, to say the character often\ndenoted by <jats:italic>\u03c7<\/jats:italic><jats:sup>(<jats:italic>n<\/jats:italic>\u22122,2)<\/jats:sup>, remains irreducible when restricted to <jats:italic>G<\/jats:italic>, then <jats:italic>n<\/jats:italic> = 4, 5 or 9 and <jats:italic>G<\/jats:italic>\u2245<jats:italic>S<\/jats:italic><jats:sub><jats:italic>3<\/jats:italic><\/jats:sub>, A<jats:sub>5<\/jats:sub>, or P\u03a3L<jats:sub>2<\/jats:sub>(8), respectively, or <jats:italic>G<\/jats:italic> is 4\u2010transitive.<\/jats:p>","DOI":"10.1155\/2011\/757134","type":"journal-article","created":{"date-parts":[[2011,8,23]],"date-time":"2011-08-23T20:38:39Z","timestamp":1314131919000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Character Condition for Quadruple Transitivity"],"prefix":"10.1155","volume":"2011","author":[{"given":"S.","family":"Aldhafeeri","sequence":"first","affiliation":[]},{"given":"R. T.","family":"Curtis","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,8,23]]},"reference":[{"key":"e_1_2_4_1_2","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1017\/S0027763000002269","article-title":"On multiple transitivity of permutation groups","volume":"18","author":"Tsuzuku T.","year":"1961","journal-title":"Nagoya Mathematical Journal"},{"key":"e_1_2_4_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021\u20108693(75)90174\u2010X"},{"key":"e_1_2_4_3_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3\u201031.4.457"},{"key":"e_1_2_4_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021\u20108693(87)90251\u20101"},{"key":"e_1_2_4_5_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002\u20109939\u20101975\u20100357563\u2010X"},{"key":"e_1_2_4_6_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814532"},{"key":"e_1_2_4_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0067708"},{"key":"e_1_2_4_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01111290"},{"key":"e_1_2_4_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01113919"},{"key":"e_1_2_4_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01112361"},{"key":"e_1_2_4_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-64981-3"},{"key":"e_1_2_4_12_2","unstructured":"AldhafeeriS. Characters of multiply transitive groups Ph.D. thesis 2009 University of Birmingham."},{"volume-title":"Group Theory","year":"1964","author":"Scott W. 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