Endomorphisms of Relatively Hyperbolic Groups
Endomorphisms of Relatively Hyperbolic Groups
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DOI：
10.1142/s0218196708004305
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发表时间：
2008-02
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通讯作者：
I. Belegradek;A. Szczepański
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作者：
I. Belegradek;A. Szczepański
本文将Paulin和Rips-Sela关于双曲群自同态的一些结果推广到相对双曲群，特别证明了以下结果。·如果G是一个具有细长抛物子群的非初等相对双曲群，且G不是余霍普夫群或Out（G）是无限的，则G在一个细长群上分裂。·若H是相对双曲群的非抛物子群，且若在一棵树上的等距H作用是平凡的，则H是霍普夫群。·如果G是一个非初等相对双曲群，其周边子群是双曲生成的，则G有一个非初等相对双曲商是霍普夫的。·对于某个具有Kazhdan性质（T）的群H，任何一个非对称群同构于Out（H）的一个有限指数子群。(This[001 pdf 1st-31 files]锐化奥利维尔-怀斯的结果）。
We generalize some results of Paulin and Rips-Sela on endomorphisms of hyperbolic groups to relatively hyperbolic groups, and in particular prove the following. • If G is a nonelementary relatively hyperbolic group with slender parabolic subgroups, and either G is not co-Hopfian or Out(G) is infinite, then G splits over a slender group. • If H is a nonparabolic subgroup of a relatively hyperbolic group, and if any isometric H-action on an ℝ-tree is trivial, then H is Hopfian. • If G is a nonelementary relatively hyperbolic group whose peripheral subgroups are finitely generated, then G has a nonelementary relatively hyperbolic quotient that is Hopfian. • Any finitely presented group is isomorphic to a finite index subgroup of Out(H) for some group H with Kazhdan property (T). (This sharpens a result of Ollivier–Wise).