Zobrazeno 1 - 10
of 140
pro vyhledávání: '"Reid, Colin D."'
Autor:
Reid, Colin D., Smith, Simon M.
The primary tool for analysing groups acting on trees is Bass--Serre Theory. It is comprised of two parts: a decomposition result, in which an action is decomposed via a graph of groups, and a construction result, in which graphs of groups are used t
Externí odkaz:
http://arxiv.org/abs/2309.05065
Autor:
Reid, Colin D.
Let $G$ be a group acting $2$-transitively on the boundary of a locally finite tree, and exclude the situation (which is a genuine exception) where $G$ has both $\mathrm{P}\Gamma\mathrm{L}_3(4)$ and $\mathrm{P}\Gamma\mathrm{L}_3(5)$ as local actions.
Externí odkaz:
http://arxiv.org/abs/2301.09078
Autor:
Reid, Colin D.
Publikováno v:
Journal of Group Theory, vol. 27, no. 4, 2024, pp. 651-712.
Let $\Omega$ be a set equipped with an equivalence relation $\sim$; we refer to the equivalence classes as blocks of $\Omega$. A permutation group $G \le \mathrm{Sym}(\Omega)$ is $k$-by-block-transitive if $\sim$ is $G$-invariant, with at least $k$ b
Externí odkaz:
http://arxiv.org/abs/2211.06848
A locally normal subgroup in a topological group is a subgroup whose normaliser is open. In this paper, we provide a detailed description of the large-scale structure of closed locally normal subgroups of complete Kac-Moody groups over finite fields.
Externí odkaz:
http://arxiv.org/abs/2112.04760
We establish a new connection between local and large-scale structure in compactly generated totally disconnected locally compact (t.d.l.c.) groups $G$, finding a sufficient condition for $G$ to have more than one end in terms of its compact subgroup
Externí odkaz:
http://arxiv.org/abs/2111.07066
Autor:
Reid, Colin D.
Motivated by the problem of finding a "well-foundedness principle" for totally disconnected, locally compact (t.d.l.c.) groups, we introduce a class $\mathscr{E}^{\mathscr{S}}$ of t.d.l.c. groups, containing P. Wesolek's class $\mathscr{E}$ of (regio
Externí odkaz:
http://arxiv.org/abs/2108.02952
Autor:
Reid, Colin D.
We obtain a characterization of totally disconnected, locally compact groups $G$ with the following property: given a locally normal subgroup $K$ of $G$, then there is an open subgroup of $K$ that is a direct factor of an open subgroup of $G$. This p
Externí odkaz:
http://arxiv.org/abs/2107.05329
Autor:
Reid, Colin D.
In a previous article by the author and P. Wesolek, it was shown that a compactly generated locally compact group $G$ admits a finite normal series $(G_i)$ in which the factors are compact, discrete or irreducible in the sense that no closed normal s
Externí odkaz:
http://arxiv.org/abs/2106.15180
Autor:
Reid, Colin D.
We classify the locally compact second-countable (l.c.s.c.) groups $A$ that are abelian and topologically characteristically simple. All such groups $A$ occur as the monolith of some soluble l.c.s.c. group $G$ of derived length at most $3$; with know
Externí odkaz:
http://arxiv.org/abs/2006.03925
Autor:
Garrido, Alejandra, Reid, Colin D.
Publikováno v:
Bull. London Math. Soc., 53 (2021): 1228-1248
This work is motivated by the problem of finding locally compact group topologies for piecewise full groups (a.k.a.~ topological full groups). We determine that any piecewise full group that is locally compact in the compact-open topology on the grou
Externí odkaz:
http://arxiv.org/abs/2005.08167