On endomorphisms of automatic groups

被引：0

作者：

Carvalho, Andre ^{[1
]}

机构：

[1] Univ Porto, Ctr Math, P-4169007 Porto, Portugal

来源：

ANNALES MATHEMATIQUES DU QUEBEC | 2024年 / 48卷 / 01期

关键词：

Automatic groups; Endomorphisms; Bounded reduction; Equalizer; Fixed subgroup; Centralizer; AUTOMORPHISMS;

D O I：

10.1007/s40316-022-00196-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend the definition of the bounded reduction property to endomorphisms of automatic group and find conditions for it to hold. We study endomorphisms with L-quasiconvex image and prove that those with finite kernel satisfy a synchronous version of the bounded reduction property. Finally, we use these techniques to prove L-quasiconvexity of the equalizer of two endomorphisms under certain (strict) conditions.

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页码：21 / 44

页数：24

相关论文

共 19 条

[1] Holder Conditions for Endomorphisms of Hyperbolic Groups [J].

Araujo, Vitor ;

Silva, Pedro V. .

COMMUNICATIONS IN ALGEBRA, 2016, 44 (10) :4483-4503

[2] TRAIN TRACKS AND AUTOMORPHISMS OF FREE GROUPS [J].

BESTVINA, M ;

HANDEL, M .

ANNALS OF MATHEMATICS, 1992, 135 (01) :1-51

[3] An algorithm for finding a basis of the fixed point subgroup of an automorphism of a free group [J].

Bogopolski, Oleg ;

Maslakova, Olga .

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2016, 26 (01) :29-67

[4]

Carvalho A., PREPRINT

[5] On uniformly continuous endomorphisms of hyperbolic groups [J].

Carvalho, Andre .

JOURNAL OF ALGEBRA, 2022, 602 :197-223

[6] AUTOMORPHISMS OF FREE GROUPS HAVE FINITELY GENERATED FIXED-POINT SETS [J].

COOPER, D .

JOURNAL OF ALGEBRA, 1987, 111 (02) :453-456

[7]

Epstein D., 1992, WORD PROCESSING GROU

[8] FIXED-POINTS OF AUTOMORPHISMS OF FREE GROUPS [J].

GERSTEN, SM .

ADVANCES IN MATHEMATICS, 1987, 64 (01) :51-85

[9] RATIONAL SUBGROUPS OF BIAUTOMATIC GROUPS [J].

GERSTEN, SM ;

SHORT, HB .

ANNALS OF MATHEMATICS, 1991, 134 (01) :125-158

[10] Automaticity for graphs of groups [J].

Hermiller, Susan ;

Holt, Derek ;

Rees, Sarah ;

Susse, Tim .

GROUPS GEOMETRY AND DYNAMICS, 2021, 15 (02) :503-551