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arXiv · 0805.4835

Associativity of the Commutator Operation in Groups

Fernando Guzman
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Abstract

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.

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Fernando Guzman. 2008-05-30. Associativity of the Commutator Operation in Groups. https://arxiv.org/abs/0805.4835

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