On endomorphisms of free groups that preserve primitivity

被引：14
作者：
Ivanov, SV [1 ]
机构：
[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA
来源：
ARCHIV DER MATHEMATIK | 1999年 / 72卷 / 02期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1007/s000130050309
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is proven that if phi is an endomorphism of a free group F-n = < x(1),...,x(n)> of rank n such that phi(u) is primitive whenever so is u is an element of F-n and phi(F-n) contains a primitive pair (i.c., a pair alpha(x(1)), alpha(x(2)) with alpha is an element of Aut F-n), then phi is an automorphism. Also, every endomorphism of F-2 that preserves primitivity is an automorphism.
引用
收藏
页码：92 / 100
页数：9
相关论文
共 50 条
[31]   PRIMITIVITY IN REPRESENTATIONS OF POLYCYCLIC GROUPS [J].
HARPER, DL .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1980, 88 (JUL) :15-31
[32]   Automorphic and endomorphic reducibility and primitive endomorphisms of free metabelian groups [J].
Gupta, CK ;
Timoshenko, EI .
COMMUNICATIONS IN ALGEBRA, 1997, 25 (10) :3057-3070
[33]   Iwip endomorphisms of free groups and fixed points of graph selfmaps [J].
Wang, Peng ;
Zhang, Qiang .
JOURNAL OF GROUP THEORY, 2025, 28 (04) :835-853
[34]   On the dynamics of extensions of free-abelian times free groups endomorphisms to the completion [J].
Carvalho, Andre .
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2022, 65 (03) :705-735
[35]   Pseudocharacters on free groups, invariant with respect to some types of endomorphisms [J].
Kagan D.Z. .
Journal of Mathematical Sciences, 2012, 186 (4) :644-650
[36]   ON TORSION - FREE ABELIAN GROUPS WITH UA-RINGS OF ENDOMORPHISMS [J].
Chistyakov, D. S. ;
Lyubimcev, O., V .
VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-MATEMATIKA I MEKHANIKA-TOMSK STATE UNIVERSITY JOURNAL OF MATHEMATICS AND MECHANICS, 2011, (14) :55-58
[37]   ENDOMORPHISMS OF FIBERED GROUPS [J].
MAXSON, CJ ;
PILZ, GF .
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1989, 32 :127-129
[38]   Primitivity of group rings of non-elementary torsion-free hyperbolic groups [J].
Solie, Brent B. .
JOURNAL OF ALGEBRA, 2018, 493 :438-443
[39]   On endomorphisms of semilattices of groups [J].
Samman, M ;
Meldrum, JDP .
ALGEBRA COLLOQUIUM, 2005, 12 (01) :93-100
[40]   Endomorphisms of Kleinian groups [J].
Delzant, T ;
Potygailo, L .
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2003, 13 (02) :396-436
12345