Maximal group actions on compact oriented surfaces

JOURNAL OF ALGEBRA

卷:472

Article

Peterson, Valerie¹  Russell, Jacob²  Wootton, Aaron¹ 

[1] Univ Portland, 5000 Willamette Blvd, Portland, OR 97203 USA

[2] CUNY, Grad Ctr, 365 5th Ave,8th Fl, New York, NY 10016 USA

关键词: Automorphism;    Compact Riemann surface;    Mapping class group;   

DOI  :  10.1016/j.jalgebra.2016.10.004

来源: Elsevier

【 摘 要 】

Suppose S is a compact oriented surface of genus >= 2 and C-p is a group of orientation preserving automorphisms of S of prime order p >= 5. We show that there is always a finite supergroup G > C-p of orientation preserving automorphisms of S except when the genus of S/C-p, is minimal (or equivalently, when the number of fixed points of C-p is maximal). Moreover, we exhibit an infinite sequence of genera within which any given action of C-p on S implies C-p is contained in some finite supergroup and demonstrate for genera outside of this sequence the existence of at least one C-p-action for which C-p is not contained in any such finite supergroup (for sufficiently large sigma). (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free