Associativity of the Commutator Operation in Groups

Details Associativity of the Commutator Operation in Groups Associativity of the Commutator Operation in Groups

2008-05-30

arxiv.org/abs/0805.4835v1

Mathematics

Group Theory

8 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Associativity of the Commutator Operation in Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Associativity of the Commutator Operation in Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Associativity of the Commutator Operation in Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-319309