Isomorphisms of Brin-Higman-Thompson groups
نویسندگان
چکیده
منابع مشابه
Cohomological Finiteness Properties of the Brin-thompson-higman Groups 2v and 3v
We show that Brin’s generalisations 2V and 3V of the Thompson-Higman group V are of type FP∞. Our methods also give a new proof that both groups are finitely presented.
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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...
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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.
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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...
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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...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2013
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-013-0042-7