Maximal group actions on compact oriented surfaces

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• 作者：Valerie Peterson^a ; ¹ ; ^{petersov@up.edu} ; Jacob Russell^b ; ¹ ; ^{jrussellmadonia@gradcenter.cuny.edu} ; Aaron Wootton^a ; ¹ ; ^{wootton@up.edu}
• 关键词：Automorphism ; Compact Riemann surface ; Mapping class group
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：472
• 期：Complete
• 页码：1-14
• 全文大小：355 K
• 卷排序：472

文摘

Suppose S   is a compact oriented surface of genus σ≥2σ≥2 and CpCp is a group of orientation preserving automorphisms of S   of prime order p≥5p≥5. We show that there is always a finite supergroup G>CpG>Cp of orientation preserving automorphisms of S   except when the genus of S/CpS/Cp is minimal (or equivalently, when the number of fixed points of CpCp is maximal). Moreover, we exhibit an infinite sequence of genera within which any given action of CpCp on S   implies CpCp is contained in some finite supergroup and demonstrate for genera outside of this sequence the existence of at least one CpCp-action for which CpCp is not contained in any such finite supergroup (for sufficiently large σ).