The group fixed by a family of endomorphisms of a surface group

JOURNAL OF ALGEBRA

卷:417

Article

Wu, Jianchun¹  Zhang, Qiang² 

[1] Soochow Univ, Dept Math, Suzhou 215006, Peoples R China

[2] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China

关键词: Fixed subgroups;    Intersections;    Endomorphisms;    Surface groups;    Inert;   

DOI  :  10.1016/j.jalgebra.2014.07.003

来源: Elsevier

【 摘 要 】

For a closed surface S with x(S) < 0, we show that the fixed subgroup of a family B of endomorphisms of pi(1)(S) has rank Fix B <= rank pi(1)(S). In particular, if B contains a non-epimorphic endomorphism, then rank Fix B <= 1/2 rank pi(1)(S). We also show that geometric subgroups of pi(1)(S) are inert, and hence the fixed subgroup of a family of epimorphisms of pi(1)(S) is also inert. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free