Geometric presentations for Thompson's groups

Details Geometric presentations for Thompson's groups Geometric presentations for Thompson's groups

2004-07-07

arxiv.org/abs/math/0407096v2

Journal of Pure and Applied Algebra 203 (2005) 1-44

Mathematics

Group Theory

Scientific paper

We prove that Thompson's groups $F$ and $V$ are the geometry groups of associativity, and of associativity together with commutativity, respectively. We deduce new presentations of $F$ and $V$. These presentations lead to considering a certain subgroup of $V$ and an extension of this subgroup. We prove that the latter are the geometry groups of associativity together with the law $x(yz) = y(xz)$, and of associativity together with a twisted version of this law involving self-distributivity, respectively.

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