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pro vyhledávání: '"Timothy C. Burness"'
Autor:
TIMOTHY C. BURNESS, DONNA M. TESTERMAN
Publikováno v:
Forum of Mathematics, Sigma, Vol 7 (2019)
Let $G$ be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic $p>0$ and let $X=\text{PSL}_{2}(p)$ be a subgroup of $G$ containing a regular unipotent element $x$ of $G$. By a theorem of Testerman
Externí odkaz:
https://doaj.org/article/4f872e510235446dae0d5af5e64de602
Publikováno v:
Forum of Mathematics, Sigma, Vol 5 (2017)
Let $G$ be a finite almost simple group. It is well known that $G$ can be generated by three elements, and in previous work we showed that 6 generators suffice for all maximal subgroups of $G$ . In this paper, we consider subgroups at the next lev
Externí odkaz:
https://doaj.org/article/ad118de59197449da59284dae8146654
Autor:
Timothy C. Burness, Michael Giudici
A classical theorem of Jordan states that every finite transitive permutation group contains a derangement. This existence result has interesting and unexpected applications in many areas of mathematics, including graph theory, number theory and topo
Autor:
Timothy C. Burness, Hong Yi Huang
Publikováno v:
Burness, T & Huang, H Y 2022, ' On the Saxl graphs of primitive groups with soluble stabilisers ', Algebraic Combinatorics, vol. 5, no. 5, pp. 1053-1087 . https://doi.org/10.5802/alco.238
Let $G$ be a transitive permutation group on a finite set $\Omega$ and recall that a base for $G$ is a subset of $\Omega$ with trivial pointwise stabiliser. The base size of $G$, denoted $b(G)$, is the minimal size of a base. If $b(G)=2$ then we can
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::77d2fbe1783e00657e3226a52df28680
https://doi.org/10.5802/alco.238
https://doi.org/10.5802/alco.238
Autor:
Timothy C. Burness, Aner Shalev
Publikováno v:
Journal of Algebra. 607:160-185
Fix a positive integer $d$ and let $\Gamma_d$ be the class of finite groups without sections isomorphic to the alternating group $A_d$. The groups in $\Gamma_d$ were studied by Babai, Cameron and P\'{a}lfy in the 1980s and they determined bounds on t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df8a5ae9ab1c1a647f5ae139868881d5
https://doi.org/10.1016/j.jalgebra.2021.08.012
https://doi.org/10.1016/j.jalgebra.2021.08.012
Publikováno v:
Burness, T, Lucchini, A & Nemmi, D 2023, ' On the soluble graph of a finite group ', Journal of Combinatorial Theory, Series A, vol. 194, 105708 . https://doi.org/10.1016/j.jcta.2022.105708
Let $G$ be a finite insoluble group with soluble radical $R(G)$. In this paper we investigate the soluble graph of $G$, which is a natural generalisation of the widely studied commuting graph. Here the vertices are the elements in $G \setminus R(G)$,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::42ef9ee3fbac6f3f688a333dd8c41eee
https://hdl.handle.net/11577/3467933
https://hdl.handle.net/11577/3467933
Autor:
Scott Harper, Timothy C. Burness
Publikováno v:
Burness, T C & Harper, S 2020, ' Finite groups, 2-generation and the uniform domination number ', Israel Journal of Mathematics, vol. 239, pp. 271-367 . https://doi.org/10.1007/s11856-020-2050-8
University of St Andrews CRIS
University of St Andrews CRIS
Let $G$ be a finite $2$-generated non-cyclic group. The spread of $G$ is the largest integer $k$ such that for any nontrivial elements $x_1, \ldots, x_k$, there exists $y \in G$ such that $G = \langle x_i, y\rangle$ for all $i$. The more restrictive
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::406aef69c1e9b5b32b677f77ce8d7e0f
https://doi.org/10.1007/s11856-020-2050-8
https://doi.org/10.1007/s11856-020-2050-8
Let $G$ be a finite group, let $H$ be a core-free subgroup and let $b(G,H)$ denote the base size for the action of $G$ on $G/H$. Let $\alpha(G)$ be the number of conjugacy classes of core-free subgroups $H$ of $G$ with $b(G,H) \geqslant 3$. We say th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d66b42109a89d7d5de5c1d536d7e145f
Autor:
Timothy C. Burness, Hong Yi Huang
Publikováno v:
Burness, T & Huang, H Y 2023, ' On base sizes for primitive groups of product type ', Journal of Pure and Applied Algebra, vol. 227, no. 3, 107228 . https://doi.org/10.1016/j.jpaa.2022.107228
Let $G \leqslant {\rm Sym}(\Omega)$ be a finite permutation group and recall that the base size of $G$ is the minimal size of a subset of $\Omega$ with trivial pointwise stabiliser. There is an extensive literature on base sizes for primitive groups,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::86b4ee05c790bfb47176a0d8899a5f88
https://doi.org/10.1016/j.jpaa.2022.107228
https://doi.org/10.1016/j.jpaa.2022.107228
Autor:
Timothy C. Burness
Publikováno v:
Burness, T C 2021, ' Base sizes for primitive groups with soluble stabilisers ', Algebra and Number Theory, vol. 15, no. 7, pp. 1755-1807 . https://doi.org/10.2140/ant.2021.15.1755
Let $G$ be a finite primitive permutation group on a set $\Omega$ with point stabiliser $H$. Recall that a subset of $\Omega$ is a base for $G$ if its pointwise stabiliser is trivial. We define the base size of $G$, denoted $b(G,H)$, to be the minima
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b75dde9329e1fdccbb213f274ba6eafe
https://hdl.handle.net/1983/03f9449b-492d-496e-bf24-dcf5d12f47d0
https://hdl.handle.net/1983/03f9449b-492d-496e-bf24-dcf5d12f47d0