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of 113
pro vyhledávání: '"Bleak, Collin"'
We show that R. Thompson's group $T$ is a maximal subgroup of the group $V$. The argument provides examples of foundational calculations which arise when expressing elements of $V$ as products of transpositions of basic clopen sets in Cantor space $\
Externí odkaz:
http://arxiv.org/abs/2409.12621
The 1973 Boone-Higman conjecture predicts that every finitely generated group with solvable word problem embeds in a finitely presented simple group. In this paper, we show that hyperbolic groups satisfy this conjecture, that is, each hyperbolic grou
Externí odkaz:
http://arxiv.org/abs/2309.06224
A conjecture of Boone and Higman from the 1970's asserts that a finitely generated group $G$ has solvable word problem if and only if $G$ can be embedded into a finitely presented simple group. We comment on the history of this conjecture and survey
Externí odkaz:
http://arxiv.org/abs/2306.16356
Autor:
Belk, James, Bleak, Collin
The Boone--Higman conjecture is that every recursively presented group with solvable word problem embeds in a finitely presented simple group. We discuss a brief history of this conjecture and work towards it. Along the way we describe some classes o
Externí odkaz:
http://arxiv.org/abs/2306.14863
Autor:
Bleak, Collin, Olukoya, Feyishayo
We address the following open problem, implicit in the 1990 article "Automorphisms of one-sided subshifts of finite type" of Boyle, Franks and Kitchens (BFK): "Does there exists an element $\psi$ in the group of automorphisms of the one-sided shift $
Externí odkaz:
http://arxiv.org/abs/2301.13570
We introduce the concept of a type system~$\Part$, that is, a partition on the set of finite words over the alphabet~$\{0,1\}$ compatible with the partial action of Thompson's group~$V$, and associate a subgroup~$\Stab{V}{\Part}$ of~$V$. We classify
Externí odkaz:
http://arxiv.org/abs/2206.12631
Every finite simple group can be generated by two elements and, in fact, every nontrivial element is contained in a generating pair. Groups with this property are said to be $\frac{3}{2}$-generated, and the finite $\frac{3}{2}$-generated groups were
Externí odkaz:
http://arxiv.org/abs/2206.05316
Let $\mathfrak{C}$ be some Cantor space. We study groups of homeomorphisms of $\mathfrak{C}$ which are vigorous, or, which are flawless, where we introduce both of these terms here. We say a group $G\leq \operatorname{Homeo}(\mathfrak{C})$ is $vigoro
Externí odkaz:
http://arxiv.org/abs/2008.04791
In this article, we further explore the nature of a connection between the groups of automorphisms of full shift spaces and the groups of outer automorphisms of the Higman--Thompson groups $\{G_{n,r}\}$. We show that the quotient of the group of auto
Externí odkaz:
http://arxiv.org/abs/2006.01466
Publikováno v:
Discrete Analysis 2021:15, 35pp
Let $1 \le r < n$ be integers. We give a proof that the group $\mathop{\mathrm{Aut}}({X_{n}^{\mathbb{N}}, \sigma_{n}})$ of automorphisms of the one-sided shift on $n$ letters embeds naturally as a subgroup $\mathcal{H}_{n}$ of the outer automorphism
Externí odkaz:
http://arxiv.org/abs/2004.08478