THE R∞ PROPERTY FOR ABELIAN GROUPS

被引：0

作者：

Dekimpe, Karel ^{[1
]}

Goncalves, Daciberg ^{[2
]}

机构：

[1] KU Leuven Kulak, E Sabbelaan 53, B-8500 Kortrijk, Belgium

[2] Univ Sao Paulo, Dept Matemat IME, BR-05314970 Sao Paulo, Brazil

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2015年 / 46卷 / 02期

关键词：

Reidemeister number; twisted conjugacy classes; Reidemeister classes; R infinity property; Abelian group; TWISTED CONJUGACY CLASSES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is well known there is no finitely generated abelian group which has the R infinity property. We will show that also many non-finitely generated abelian groups do not have the R infinity property, but this does not hold for all of them! In fact we construct an uncountable number of infinite countable abelian groups which do have the R infinity. property. We also construct an abelian group such that the cardinality of the Reidemeister classes is uncountable for any automorphism of that group.

引用

页码：773 / 784

页数：12

共 11 条

[1] The R∞ property for free groups, free nilpotent groups and free solvable groups
Dekimpe, Karel
Goncalves, Daciberg
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2014, 46 : 737 - 746
[2] Fel'shtyn A, 2000, MEM AM MATH SOC, V147, P1
[3] Twisted conjugacy classes in saturated weakly branch groups
Fel'shtyn, Alexander
Leonov, Yuriy
Troitsky, Evgenij
[J]. GEOMETRIAE DEDICATA, 2008, 134 (01) : 61 - 73
[4] New directions in Nielsen-Reidemeister theory
Fel'shtyn, Alexander
[J]. TOPOLOGY AND ITS APPLICATIONS, 2010, 157 (10-11) : 1724 - 1735
[5] Fuchs L., 1970, Infinite Abelian Groups. Vol. I
[6] Jiang BJ, 2005, HANDBOOK OF TOPOLOGICAL FIXED POINT THEORY, P617, DOI 10.1007/1-4020-3222-6_16
[7] KAPLANSKY I., 1970, INFINITE ABELIAN GRO
[8] TWISTED CONJUGACY CLASSES IN LATTICES IN SEMISIMPLE LIE GROUPS
Mubeena, T.
Sankaran, P.
[J]. TRANSFORMATION GROUPS, 2014, 19 (01) : 159 - 169
[9] Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups
Mubeena, T.
Sankaran, P.
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2014, 57 (01): : 132 - 140
[10] Twisted conjugacy classes in general and special linear groups
Nasybullov, T. R.
[J]. ALGEBRA AND LOGIC, 2012, 51 (03) : 220 - 231

← 1 2 →