Twisted Conjugacy in Houghton's groups

Charles Cox

doi:10.1016/j.jalgebra.2017.07.013

Twisted Conjugacy in Houghton's groups

Charles Cox

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

8 Citations (Scopus)

275 Downloads (Pure)

Abstract

For a fixed , the Houghton group consists of bijections of that are ‘eventually translations’ of each copy of . The Houghton groups have been shown to have solvable conjugacy problem. In general, solvable conjugacy problem does not imply that all finite extensions and finite index subgroups have solvable conjugacy problem. Our main theorem is that a stronger result holds: for any and any group G commensurable to , G has solvable conjugacy problem.

Original language	English
Pages (from-to)	390-436
Number of pages	47
Journal	Journal of Algebra
Volume	490
Early online date	1 Aug 2017
DOIs	https://doi.org/10.1016/j.jalgebra.2017.07.013
Publication status	Published - 15 Nov 2017

Keywords

Uniform twisted conjugacy problem
Houghton group
Permutation group
Orbit decidability
Conjugacy problem for commensurable groups
Computable centralisers

Access to Document

10.1016/j.jalgebra.2017.07.013

Full-text PDF (accepted author manuscript)
This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Elsevier at https://doi.org/10.1016/j.jalgebra.2017.07.013 . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 493 KBLicence: CC BY-NC-ND

Handle.net

Persistent link

Cite this

@article{8e0bcab8eb8d46929fb73ff30645b3d1,

title = "Twisted Conjugacy in Houghton's groups",

abstract = "For a fixed , the Houghton group consists of bijections of that are {\textquoteleft}eventually translations{\textquoteright} of each copy of . The Houghton groups have been shown to have solvable conjugacy problem. In general, solvable conjugacy problem does not imply that all finite extensions and finite index subgroups have solvable conjugacy problem. Our main theorem is that a stronger result holds: for any and any group G commensurable to , G has solvable conjugacy problem.",

keywords = "Uniform twisted conjugacy problem, Houghton group, Permutation group, Orbit decidability, Conjugacy problem for commensurable groups, Computable centralisers",

author = "Charles Cox",

year = "2017",

month = nov,

day = "15",

doi = "10.1016/j.jalgebra.2017.07.013",

language = "English",

volume = "490",

pages = "390--436",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Twisted Conjugacy in Houghton's groups

AU - Cox, Charles

PY - 2017/11/15

Y1 - 2017/11/15

N2 - For a fixed , the Houghton group consists of bijections of that are ‘eventually translations’ of each copy of . The Houghton groups have been shown to have solvable conjugacy problem. In general, solvable conjugacy problem does not imply that all finite extensions and finite index subgroups have solvable conjugacy problem. Our main theorem is that a stronger result holds: for any and any group G commensurable to , G has solvable conjugacy problem.

AB - For a fixed , the Houghton group consists of bijections of that are ‘eventually translations’ of each copy of . The Houghton groups have been shown to have solvable conjugacy problem. In general, solvable conjugacy problem does not imply that all finite extensions and finite index subgroups have solvable conjugacy problem. Our main theorem is that a stronger result holds: for any and any group G commensurable to , G has solvable conjugacy problem.

KW - Uniform twisted conjugacy problem

KW - Houghton group

KW - Permutation group

KW - Orbit decidability

KW - Conjugacy problem for commensurable groups

KW - Computable centralisers

UR - https://arxiv.org/abs/1410.7051

U2 - 10.1016/j.jalgebra.2017.07.013

DO - 10.1016/j.jalgebra.2017.07.013

M3 - Article (Academic Journal)

SN - 0021-8693

VL - 490

SP - 390

EP - 436

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Twisted Conjugacy in Houghton's groups

Abstract

Keywords

Access to Document

Handle.net

Other files and links

Fingerprint

Cite this