Geometric presentations for Thompson's groups
Copyright policy )Geometric presentations for Thompson's groups
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.
geometry groups, partial group action, 20F36, commutativity, Group Theory (math.GR), [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], FOS: Mathematics, braid groups, Sets with a single binary operation (groupoids), infinite generating sets, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR], braided Thompson groups, Generators, relations, and presentations of groups, Algebra and Number Theory, presentations, algebraic law, Thompson group \(V\), 20B07, Braid groups; Artin groups, geometry group, left self-distributive operations, MSC: 20F05, 20F36, 20B07, Coxeter relations, Thompson group \(F\), associativity, generators, Thompson\'s groups, Mathematics - Group Theory, MSC: 20F05
geometry groups, partial group action, 20F36, commutativity, Group Theory (math.GR), [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], FOS: Mathematics, braid groups, Sets with a single binary operation (groupoids), infinite generating sets, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR], braided Thompson groups, Generators, relations, and presentations of groups, Algebra and Number Theory, presentations, algebraic law, Thompson group \(V\), 20B07, Braid groups; Artin groups, geometry group, left self-distributive operations, MSC: 20F05, 20F36, 20B07, Coxeter relations, Thompson group \(F\), associativity, generators, Thompson\'s groups, Mathematics - Group Theory, MSC: 20F05
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