Free partially commutative structures

@article{Duchamp1993FreePC,
  title={Free partially commutative structures},
  author={G{\'e}rard H. E. Duchamp and Daniel Krob},
  journal={Journal of Algebra},
  year={1993},
  volume={156},
  pages={318-361}
}
Abstract In this paper, we study algebraic structures defined by a presentation of the form 〈 A; ab = ba for (a, b) ∈ I 〉. We show that these relators are the only one that can be interpreted as both monoid and Lie relators. We also study the free partially commutative monoids, Lie algebras, and groups: in all of these cases, we show how to obtain decomposition results for these structures into the corresponding free structures. 
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