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Discrete Group
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Twisted Conjugacy Classes
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Twisted Conjugacy Classes in Wreath Products
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Twisted Burnside theorem for type II_1 groups: an example
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Twisted BurnsideFrobenius theory for discrete groups
Twisted BurnsideFrobenius theory for discrete groups,10.1515/CRELLE.2007.097,Journal Fur Die Reine Und Angewandte Mathematik,ALEXANDER FEL' SHTYN,Evg
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Twisted BurnsideFrobenius theory for discrete groups
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Citations: 12
)
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ALEXANDER FEL' SHTYN
,
Evgenij Troitsky
For a wide class of groups including polycyclic and finitely generated polynomial growth groups it is proved that the Reidemeister number of an automorphism f is equal to the number of finitedimensional fixed points of the induced map f^ on the unitary dual, if one of these numbers is finite. This theorem is a natural generalization of the classical BurnsideFrobenius theorem to infinite groups. This theorem also has important consequences in
topological dynamics
and in some sense is a reply to a remark of J.P. Serre. The main technical results proved in the paper yield a tool for a further progress.
Journal:
Journal Fur Die Reine Und Angewandte Mathematik  J REINE ANGEW MATH
, vol. 2007, no. 613, pp. 193210, 2007
DOI:
10.1515/CRELLE.2007.097
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Citation Context
(6)
...Fel’shtyn and Troitsky [
13
] showed that this equality does hold for virtually polycyclic groups if one of the numbers in the equality is nite...
Nic Koban
,
et al.
A relationship between twisted conjugacy classes and the geometric inv...
...of papers [25, 22, 32, 33, 95, 30, 28,
31
, 29, 54] In the paper [35] we...
...striction) (Definitions 2.3 and 2.5). This notion was used in [
31
] to...
...finite groups are strongly twisted conjugacy separable groups [
31
, 35]...
...gacy classes). Then G is a twisted conjugacy separable group [
31
, 35]...
...(3) Examples of groups, which are not twisted conjugacy separable: HNN, Ivanov and Osin groups [
31
]...
...is formed by the finitedimensional representations [
31
, 35]...
...Congruences for Reidemeister numbers[
31
]: Let φ : G → G be an...
...[25, 32, 33, 95,
31
, 29, 54] has yet to be verified...
...This notion is closely related to the notion RP(φ) introduced in [
31
]...
...Definition 2.4. [
31
] We say that a group G has the property RP if for...
...Theorem 2.2. [
31
] Suppose, R(φ) < ∞. Then G is φconjugacy sep...
...Theorem 2.4. [
31
] Let F : → K be a morphism onto a finite group...
...Theorem 2.6. [
31
] Any polycyclicbyfinite group is a strongly twisted...
...Theorem 2.7. [
31
] Suppose, there exists a commutative diagram...
...Theorem 2.8. [
31
] Let G be an φconjugacy separable group .Then...
Alexander Fel'shtyn
.
New directions in Nielsen–Reidemeister theory
...[
12
].) In particular, groups that are quasiisometric to...
DACIBERG GONCALVES
,
et al.
Twisted conjugacy classes in nilpotent groups
...celebrated BurnsideFrobenius theorem [10, 12, 14,
11
, 13]...
Alexander Fel'shtyn
,
et al.
Twisted conjugacy classes of automorphisms of BaumslagSolitar groups
...of the BurnsideFrobenius theorem [16, 12, 19, 20, 49,
18
, 17], that is, to show...
...conjecture [16, 19, 20, 49,
18
, 17] has yet to be verified...
ALEXANDER FEL' SHTYN
,
et al.
TWISTED CONJUGACY CLASSES IN SYMPLECTIC GROUPS, MAPPING CLASS GROUPS A...
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(26)
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,
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(
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Journal:
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Twisted Burnside theorem for type II_1 groups: an example
(
Citations: 16
)
Alexander Fel'shtyn
,
Evgenij Troitsky
,
Anatoly Vershik
Published in 2006.
On Burnside''s problem on periodic groups
(
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Publications Mathematiques De L Ihes  PUBL MATH
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Citations
(12)
A relationship between twisted conjugacy classes and the geometric invariants Ω n
Nic Koban
,
Peter Wong
Journal:
Geometriae Dedicata  GEOM DEDIC
, vol. 151, no. 1, pp. 233243, 2011
Amplification of fluorescence emission of CdSe/ZnS QDs entrapped in a sol–gel matrix, a new approach for detection of trace level of PAHs
Hong Dinh Duong
,
C. V. Gopal Reddy
,
Jong Il Rhee
,
Tuan VoDinh
Journal:
Sensors and Actuators Bchemical  SENSOR ACTUATOR BCHEM
, vol. 157, no. 1, pp. 139145, 2011
Twisted conjugacy classes in nilpotent groups
V. Roman’kov
Journal:
Journal of Pure and Applied Algebra  J PURE APPL ALG
, vol. 215, no. 4, pp. 664671, 2011
New directions in Nielsen–Reidemeister theory
Alexander Fel'shtyn
Journal:
Topology and Its Applications  TOPOL APPL
, vol. 157, no. 10, pp. 17241735, 2010
Geometry of Reidemeister classes and twisted Burnside theorem
(
Citations: 13
)
Alexander Fel'shtyn
,
Evgenij Troitsky
Journal:
Journal of Ktheory: Ktheory and Its Applications To Algebra, Geometry, and Topology
, vol. 2, no. 03, 2009