Defining relations for the Held-Higman-Thompson simple group
نویسندگان
چکیده
منابع مشابه
The 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...
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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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The co-word problem of a group G generated by a set X is defined as the set of words in X which do not represent 1 in G. We introduce a new method to decide if a permutation group has context-free co-word problem. We use this method to show, that the Higman-Thompson groups, and therefore the Houghton groups, have context-free co-word problem. We also give some examples of groups, that even have...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1974
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700043616