{"title":"An update on Hurwitz groups","authors":"M. Conder","doi":"10.1515/gcc.2010.002","DOIUrl":null,"url":null,"abstract":"Abstract A Hurwitz group is any non-trivial finite quotient of the (2, 3, 7) triangle group, that is, any non-trivial finite group generated by elements x and y satisfying x 2 = y 3 = (xy)7 = 1. Every such group G is the conformal automorphism group of some compact Riemann surface of genus g > 1, with the property that |G| = 84(g – 1), which is the maximum possible order for given genus g. This paper provides an update on what is known about Hurwitz groups and related matters, following up the author's brief survey in Bull. Amer. Math. Soc.23 (1990).","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"50","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complex. Cryptol.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/gcc.2010.002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 50
Abstract
Abstract A Hurwitz group is any non-trivial finite quotient of the (2, 3, 7) triangle group, that is, any non-trivial finite group generated by elements x and y satisfying x 2 = y 3 = (xy)7 = 1. Every such group G is the conformal automorphism group of some compact Riemann surface of genus g > 1, with the property that |G| = 84(g – 1), which is the maximum possible order for given genus g. This paper provides an update on what is known about Hurwitz groups and related matters, following up the author's brief survey in Bull. Amer. Math. Soc.23 (1990).
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
