Associativity of the Commutator Operation in Groups
| dc.creator | Guzman, Fernando | |
| dc.date | 2008-05-30 | |
| dc.date.accessioned | 2026-07-07T09:41:56Z | |
| dc.date.available | 2026-07-07T09:41:56Z | |
| dc.description | The study of associativity of the commutator operation in groups goes back to some work of Levi in 1942. In the 1960's Richard J. Thompson created a group F whose elements are representatives of the generalized associative law for an arbitrary binary operation. In 2006, Geoghegan and Guzman proved that a group G is solvable if and only if the commutator operation in G eventually satisfies ALL instances of the associative law, and also showed that many non-solvable groups do not satisfy any instance of the generalized associative law. We will address the question: Is there a non-solvable group which satisfies SOME instance of the generalized associative law? For finite groups, we prove that the answer is no. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/0805.4835 | |
| dc.identifier | http://arxiv.org/abs/0805.4835 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162002 | |
| dc.subject | Group Theory | |
| dc.subject | 20D05 (Primary); 20F16, 20N02, 20F38 (Secondary) | |
| dc.title | Associativity of the Commutator Operation in Groups | |
| dc.type | text |