Non-elementary amenable subgroups of automata groups
نویسندگان
چکیده
منابع مشابه
Non-elementary amenable subgroups of automata groups
We consider groups of automorphisms of locally finite trees, and give conditions on its subgroups that imply that they are not elementary amenable. This covers all known examples of groups that are not elementary amenable and act on the trees: groups of intermediate growths and Basilica group, by giving a more straightforward proof. Moreover, we deduce that all finitely generated branch groups ...
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This paper contributes to the study of the subgroups of Thompson’s group F by constructing a sequence of subgroups of increasing complexity. The group F is an interesting finitely presented group with a pleasant, faithful representation in the group PLo(I) of orientation preserving, piecewise linear, self homeomorphisms of the unit interval. Thus our subgroups also lie in PLo(I). The subgroups ...
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Let G be a not necessarily split reductive group scheme over a commutative ring R with 1. Given a parabolic subgroup P of G, the elementary group EP (R) is defined to be the subgroup of G(R) generated by UP (R) and UP−(R), where UP and UP− are the unipotent radicals of P and its opposite P −, respectively. It is proved that if G contains a Zariski locally split torus of rank 2, then the group E...
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ژورنال
عنوان ژورنال: Journal of Topology and Analysis
سال: 2017
ISSN: 1793-5253,1793-7167
DOI: 10.1142/s179352531850005x