Monoids that map onto the Thompson-Higman groups
نویسندگان
چکیده
منابع مشابه
Coherent Presentations of Structure Monoids and the Higman-thompson Groups
Structure monoids and groups are algebraic invariants of equational varieties. We show how to construct presentations of these objects from coherent categorifications of equational varieties, generalising several results of Dehornoy. We subsequently realise the higher Thompson groups Fn,1 and the Higman-Thompson groups Gn,1 as structure groups. We go on to obtain presentations of these groups v...
متن کاملThe homology of the Higman–Thompson groups
We prove that Thompson’s group V is acyclic, answering a 1992 question of Brown in the positive. More generally, we identify the homology of the Higman–Thompson groups Vn,r with the homology of the zeroth component of the infinite loop space of the mod n− 1 Moore spectrum. As V = V2,1, we can deduce that this group is acyclic. Our proof involves establishing homological stability with respect t...
متن کاملFinite Factor Representations of Higman-Thompson groups
We prove that the only finite factor-representations of the HigmanThompson groups {Fn,r}, {Gn,r} are the regular representations and scalar representations arising from group abelianizations. As a corollary, we obtain that any measure-preserving ergodic action of a simple Higman-Thompson group must be essentially free. Finite factor representations of other classes of groups are also discussed.
متن کاملFactorizations of the Thompson-higman Groups, and Circuit Complexity
We consider the subgroup lpGk,1 of length preserving elements of the Thompson-Higman group Gk,1 and we show that all elements of Gk,1 have a unique lpGk,1 · Fk,1 factorization. This applies to the Thompson-Higman group Tk,1 as well. We show that lpGk,1 is a “diagonal” direct limit of finite symmetric groups, and that lpTk,1 is a k ∞ Prüfer group. We find an infinite generating set of lpGk,1 whi...
متن کاملThe polycyclic monoids Pn and the Thompson groups Vn,1
We construct what we call the strong orthogonal completion Cn of the polycyclic monoid Pn on n generators. The inverse monoid Cn is congruence free and its group of units is the Thompson group Vn,1. Copies of Cn can be constructed from partitions of sets into n blocks each block having the same cardinality as the underlying set. 2000 AMS Subject Classification: 20M18, 20E32.
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ژورنال
عنوان ژورنال: Semigroup Forum
سال: 2011
ISSN: 0037-1912,1432-2137
DOI: 10.1007/s00233-011-9303-0