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A graph $X$ is said to be "unstable" if the direct product $X \times K_2$ (also called the canonical double cover of $X$) has automorphisms that do not come from automorphisms of its factors $X$ and $K_2$. It is "nontrivially unstable" if it is unsta
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c00e365818af42830a49fbfd559cebfd
http://arxiv.org/abs/2108.05893
http://arxiv.org/abs/2108.05893
Autor:
Dave Witte Morris
Publikováno v:
The Electronic Journal of Combinatorics. 28
Let $X$ and $Y$ be connected Cayley graphs on abelian groups, such that no two distinct vertices of $X$ have exactly the same neighbours, and the same is true about $Y$. We show that if the number of vertices of $X$ is relatively prime to the number
We say that a finite group G is "DRR-detecting" if, for every subset S of G, either the Cayley digraph Cay(G,S) is a digraphical regular representation (that is, its automorphism group acts regularly on its vertex set) or there is a nontrivial group
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5d323583fb3bfcb16235c8546bf40800
http://arxiv.org/abs/2005.09798
http://arxiv.org/abs/2005.09798
Autor:
Dave Witte Morris
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications.
We say that a subset $X$ quasi-isometrically boundedly generates a finitely generated group $\Gamma$ if each element $\gamma$ of a finite-index subgroup of $\Gamma$ can be written as a product $\gamma = x_1 x_2 \cdots x_r$ of a bounded number of elem
Autor:
Dave Witte Morris
Publikováno v:
Journal of Algebra Combinatorics Discrete Structures and Applications, Vol 3, Iss 1, Pp 13-30 (2016)
This note shows there are infinitely many finite groups G, such that every connected Cayley graph on G has a hamiltonian cycle, and G is not solvable. Specifically, for every prime p that is congruent to 1, modulo 30, we show there is a hamiltonian c
Autor:
Dave Witte Morris, Kirsten Wilk
Publikováno v:
The Art of Discrete and Applied Mathematics. 3:#P2.02
We provide a computer-assisted proof that if G is any finite group of order kp, where k < 48 and p is prime, then every connected Cayley graph on G is hamiltonian (unless kp = 2). As part of the proof, it is verified that every connected Cayley graph
Publikováno v:
Documenta Mathematica
Documenta Mathematica, Universität Bielefeld, 2018
Documenta Mathematica, Universität Bielefeld, 2018
We show that relative Property (T) for the abelianization of a nilpotent normal subgroup implies relative Property (T) for the subgroup itself. This and other results are a consequence of a theorem of independent interest, which states that if $H$ is
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3bc3f1783fb1cffa7d5c27b8282c241b
https://hal.archives-ouvertes.fr/hal-03424527/file/1702.01801.pdf
https://hal.archives-ouvertes.fr/hal-03424527/file/1702.01801.pdf
Autor:
Dave Witte Morris
Publikováno v:
Ars Mathematica Contemporanea. 8:1-28
We show that if G is a nontrivial, finite group of odd order, whose commutator subgroup [G,G] is cyclic of order p^m q^n, where p and q are prime, then every connected Cayley graph on G has a hamiltonian cycle.
Comment: 32 pages
Comment: 32 pages
Autor:
Dave Witte Morris, Peter A. Linnell
Publikováno v:
Groups, Geometry, and Dynamics. 8:467-478
We show that every amenable group with a locally invariant partial order has a left-invariant total order (and is therefore locally indicable). We also show that if a group G admits a left-invariant total order, and H is a locally nilpotent subgroup
Autor:
Robert J. Zimmer, Dave Witte Morris
Publikováno v:
Journal of Topology and Analysis. :115-120
We prove that SL (n, ℚ) has no nontrivial, C∞, volume-preserving action on any compact manifold of dimension strictly less than n. More generally, suppose G is a connected, isotropic, almost-simple algebraic group over ℚ, such that the simple f