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Abstract:

We present a new test for studying asphericity and diagrammatic reducibility of group presentations. Our test can be applied to prove diagrammatic reducibility in cases where the classical weight test fails. We use this criterion to generalize results of J. Howie and S.M. Gersten on asphericity of LOTs and of Adian presentations, and derive new results on solvability of equations over groups. We also use our methods to investigate a conjecture of S.V. Ivanov related to Kaplansky's problem on zero divisors: we strengthen Ivanov's result for locally indicable groups and prove a weak version of the conjecture. © 2019 Royal Society of Edinburgh.

Registro:

Documento: Artículo
Título:A new test for asphericity and diagrammatic reducibility of group presentations
Autor:Barmak, J.A.; Minian, E.G.
Filiación:Departamento de Matemática-IMAS FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Adian presentations; Asphericity; DR presentations; labelled oriented trees; locally indicable groups; weight test
Año:2019
DOI: http://dx.doi.org/10.1017/prm.2018.126
Título revista:Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Título revista abreviado:Proc. R. Soc. Edinburgh Sect. A Math.
ISSN:03082105
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_03082105_v_n_p_Barmak

Citas:

---------- APA ----------
Barmak, J.A. & Minian, E.G. (2019) . A new test for asphericity and diagrammatic reducibility of group presentations. Proceedings of the Royal Society of Edinburgh Section A: Mathematics.
http://dx.doi.org/10.1017/prm.2018.126
---------- CHICAGO ----------
Barmak, J.A., Minian, E.G. "A new test for asphericity and diagrammatic reducibility of group presentations" . Proceedings of the Royal Society of Edinburgh Section A: Mathematics (2019).
http://dx.doi.org/10.1017/prm.2018.126
---------- MLA ----------
Barmak, J.A., Minian, E.G. "A new test for asphericity and diagrammatic reducibility of group presentations" . Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2019.
http://dx.doi.org/10.1017/prm.2018.126
---------- VANCOUVER ----------
Barmak, J.A., Minian, E.G. A new test for asphericity and diagrammatic reducibility of group presentations. Proc. R. Soc. Edinburgh Sect. A Math. 2019.
http://dx.doi.org/10.1017/prm.2018.126