A new test for asphericity and diagrammatic reducibility of group presentations
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 L...
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| Formato: | INPR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03082105_v_n_p_Barmak |
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todo:paper_03082105_v_n_p_Barmak2023-10-03T15:22:48Z A new test for asphericity and diagrammatic reducibility of group presentations Barmak, J.A. Minian, E.G. Adian presentations Asphericity DR presentations labelled oriented trees locally indicable groups weight test 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. INPR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03082105_v_n_p_Barmak |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Adian presentations Asphericity DR presentations labelled oriented trees locally indicable groups weight test |
| spellingShingle |
Adian presentations Asphericity DR presentations labelled oriented trees locally indicable groups weight test Barmak, J.A. Minian, E.G. A new test for asphericity and diagrammatic reducibility of group presentations |
| topic_facet |
Adian presentations Asphericity DR presentations labelled oriented trees locally indicable groups weight test |
| description |
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. |
| format |
INPR |
| author |
Barmak, J.A. Minian, E.G. |
| author_facet |
Barmak, J.A. Minian, E.G. |
| author_sort |
Barmak, J.A. |
| title |
A new test for asphericity and diagrammatic reducibility of group presentations |
| title_short |
A new test for asphericity and diagrammatic reducibility of group presentations |
| title_full |
A new test for asphericity and diagrammatic reducibility of group presentations |
| title_fullStr |
A new test for asphericity and diagrammatic reducibility of group presentations |
| title_full_unstemmed |
A new test for asphericity and diagrammatic reducibility of group presentations |
| title_sort |
new test for asphericity and diagrammatic reducibility of group presentations |
| url |
http://hdl.handle.net/20.500.12110/paper_03082105_v_n_p_Barmak |
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