{"id":195,"date":"2009-04-10T14:11:11","date_gmt":"2009-04-10T05:11:11","guid":{"rendered":"http:\/\/mathsci.kaist.ac.kr\/~sangil\/seminar\/?p=195"},"modified":"2009-04-13T23:02:57","modified_gmt":"2009-04-13T14:02:57","slug":"20090501","status":"publish","type":"post","link":"https:\/\/mathsci.kaist.ac.kr\/~sangil\/seminar\/20090501\/","title":{"rendered":"Mitsugu Hirasaka, Finding n such that every transitive permutation group of degree n is multiplicity-free"},"content":{"rendered":"<div class=\"talk\">Finding n such that every transitive permutation group of degree n is multiplicity-free<\/div>\n<div class=\"speaker\"><a href=\"http:\/\/math.pusan.ac.kr\/3000\/3000.asp?intno=36\">Mitsugu Hirasaka<\/a><br \/> Department of Mathematics, Pusan National University, Pusan, Korea<\/a>\n<\/div>\n<div class=\"date\">2009\/5\/1 Friday 4PM-5PM<\/div>\n<div class=\"abstract\">This is a joint work with Cai-Heng Li. Let <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cmathcal%7BMF%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\mathcal{MF}' title='\\mathcal{MF}' class='latex' \/> denote the set of positive integers n such that each transitive action of degree n is multiplicity-free, and <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cmathcal%7BPQ%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\mathcal{PQ}' title='\\mathcal{PQ}' class='latex' \/> denote the set of <img src='https:\/\/s0.wp.com\/latex.php?latex=n%5Cin+%5Cmathbb%7BN%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='n\\in \\mathbb{N}' title='n\\in \\mathbb{N}' class='latex' \/> such that n=pq for some primes p, q with <img src='https:\/\/s0.wp.com\/latex.php?latex&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='' title='' class='latex' \/>p<q[\/latex] and [latex](p,q-1)=1[\/latex] where (m,l) is the greatest common divisor of m and n. Our main result shows that [latex]\\mathcal{PQ}\\backslash \\mathcal{MF}[\/latex] is the union of <center><img src='https:\/\/s0.wp.com\/latex.php?latex=%5C%7Bpq%5Cin+%5Cmathcal%7BPQ%7D%5Cmid+%28p%2Cq-2%29%3Dp%2C+q%5Cmbox%7B+is+a+Fermat+prime%7D%5C%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\{pq\\in \\mathcal{PQ}\\mid (p,q-2)=p, q\\mbox{ is a Fermat prime}\\}' title='\\{pq\\in \\mathcal{PQ}\\mid (p,q-2)=p, q\\mbox{ is a Fermat prime}\\}' class='latex' \/><\/center> and <center><img src='https:\/\/s0.wp.com\/latex.php?latex=%5C%7Bpq%5Cin+%5Cmathcal%7BPQ%7D%5Cmid+q%3D2p-1%5C%7D&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\{pq\\in \\mathcal{PQ}\\mid q=2p-1\\}' title='\\{pq\\in \\mathcal{PQ}\\mid q=2p-1\\}' class='latex' \/><\/center> where its proof owes much to classification of finite simple groups.<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Finding n such that every transitive permutation group of degree n is multiplicity-free Mitsugu Hirasaka Department of Mathematics, Pusan National University, Pusan, Korea 2009\/5\/1 Friday 4PM-5PM This is a joint work with Cai-Heng Li. Let denote the set of positive integers n such that each transitive action of degree n is multiplicity-free, and denote the [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_newsletter_tier_id":0,"jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[30,17],"tags":[35],"jetpack_publicize_connections":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Mitsugu Hirasaka, Finding n such that every transitive permutation group of degree n is multiplicity-free - KAIST Discrete Math Seminar<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathsci.kaist.ac.kr\/~sangil\/seminar\/20090501\/\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"sangil\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathsci.kaist.ac.kr\/~sangil\/seminar\/20090501\/\",\"url\":\"https:\/\/mathsci.kaist.ac.kr\/~sangil\/seminar\/20090501\/\",\"name\":\"Mitsugu Hirasaka, Finding n such that every transitive permutation group of degree n is multiplicity-free - 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