Displaying similar documents to “The chameleon groups of Richards J. Thompson: automorphisms and dynamics”

Schreier type theorems for bicrossed products

Ana Agore, Gigel Militaru (2012)

Open Mathematics

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We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups (H;G; α; β) is deformed using a combinatorial datum (σ; v; r) consisting of an automorphism σ of H, a permutation v of the set G and a transition map r: G → H in order to obtain a new matched pair (H; (G; *); α′, β′) such that there exists a σ-invariant isomorphism of groups H α⋈β G ≅H α′⋈β′ (G, *). Moreover, if we fix the group H and the automorphism σ...

On the dynamics of (left) orderable groups

Andrés Navas (2010)

Annales de l’institut Fourier

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We develop dynamical methods for studying left-orderable groups as well as the spaces of orderings associated to them. We give new and elementary proofs of theorems by Linnell (if a left-orderable group has infinitely many orderings, then it has uncountably many) and McCleary (the space of orderings of the free group is a Cantor set). We show that this last result also holds for countable torsion-free nilpotent groups which are not rank-one Abelian. Finally, we apply our methods to the...

Mutations in finite groups.

Gil, Antoni, Martínez, José R. (1994)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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Isogroups and isosubgroups.

Raúl M. Falcón, Juan Núñez (2003)

RACSAM

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The main goal of this paper is to give a mathematical foundation, serious and consistent, to some parts of . We study the isotopic liftings of groups and subgroups and we also deal with the differences between an isosubgroup and a subgroup of an isogroup. Finally, some links between this isotheory and the standard groups theory, referred to representation and equivalence relations among groups are shown.

N-determined 2-compact groups. I

Jesper M. Møller (2007)

Fundamenta Mathematicae

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This is the first part of a paper that classifies 2-compact groups. In this first part we formulate a general classification scheme for 2-compact groups in terms of their maximal torus normalizer pairs. We apply this general classification procedure to the simple 2-compact groups of the A-family and show that any simple 2-compact group that is locally isomorphic to PGL(n+1,ℂ) is uniquely N-determined. Thus there are no other 2-compact groups in the A-family than the ones we already know....