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A connected graph is called \emph{geodetic} if there is a unique geodesic between each pair of vertices. In this paper we prove that if a finitely generated group admits a Cayley graph which is geodetic, then the group must be virtually free. Before
Externí odkaz:
http://arxiv.org/abs/2311.03730
We call a graph $k$-geodetic, for some $k\geq 1$, if it is connected and between any two vertices there are at most $k$ geodesics. It is shown that any hyperbolic group with a $k$-geodetic Cayley graph is virtually-free. Furthermore, in such a group
Externí odkaz:
http://arxiv.org/abs/2211.13397
Autor:
Townsend, Kane Douglas
Let $W$ be a finite reflection group, either real or complex, and $S_\ell$ a Sylow $\ell$-subgroup of $W$. We prove the existence of a semidirect product decomposition of $N_W(S_\ell)$ in terms of the unique parabolic subgroup of $W$ minimally contai
Externí odkaz:
http://arxiv.org/abs/2211.04044
Akademický článek
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Autor:
Townsend, Kane Douglas
Publikováno v:
Communications in Algebra (2020)
Let $\ell$ be a prime divisor of the order of a finite unitary reflection group. We classify up to conjugacy the parabolic and reflection subgroups that are minimal with respect to inclusion, subject to containing an $\ell$-Sylow subgroup. The classi
Externí odkaz:
http://arxiv.org/abs/1910.14252
Autor:
Laura Townsend Kane
Written in a warm and personal style, Working in the Virtual Stacks presents an exciting future for librarians, already upon us today!
Akademický článek
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Autor:
Laura Townsend Kane
For library students, paraprofessionals, and librarians who are wondering if they have their ladder against the right wall, Straight from the Stacks fills the need for an up-to-date resource that uncovers the amazing and varied jobs available in the
Autor:
Townsend, Kane Douglas
Let $W$ be a finite reflection group, $\ell$ a prime divisor of $|W|$ and $S_\ell$ a Sylow $\ell$-subgroup of $W$. It can be shown that there exists a unique parabolic subgroup $P$ minimally containing $S_\ell$. We prove that there exists a simple sy
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c697c8ee4f4c944056a9dce3728ae757
Autor:
Townsend, Kane
In this thesis we study and classify specific subgroups in both finite reflection groups and finite groups of Lie type with the property that they minimally contain a Sylow subgroup. Connections between these minimal subgroups are investigated throug
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od_______293::fcbcc0a3a3a04d3c0f4d00b2661d51ac
https://hdl.handle.net/2123/27961
https://hdl.handle.net/2123/27961