Zobrazeno 1 - 10
of 35
pro vyhledávání: '"Freedman, Saul D."'
The synchronisation hierarchy of finite permutation groups consists of classes of groups lying between 2-transitive groups and primitive groups. This includes the class of spreading groups, which are defined in terms of sets and multisets of permuted
Externí odkaz:
http://arxiv.org/abs/2311.07846
The relational complexity of a subgroup $G$ of $\mathrm{Sym}(\Omega)$ is a measure of the way in which the orbits of $G$ on $\Omega^k$ for various $k$ determine the original action of $G$. Very few precise values of relational complexity are known. T
Externí odkaz:
http://arxiv.org/abs/2309.16111
Autor:
Freedman, Saul D.
Let $G$ be a group such that $G/Z(G)$ is finite and simple. The non-commuting, non-generating graph $\Xi(G)$ of $G$ has vertex set $G \setminus Z(G)$, with edges corresponding to pairs of elements that do not commute and do not generate $G$. We show
Externí odkaz:
http://arxiv.org/abs/2212.01616
Autor:
Freedman, Saul D.
Publikováno v:
Algebr. Comb. 6 (2023), 1395-1418
Let $G$ be a (finite or infinite) group such that $G/Z(G)$ is not simple. The non-commuting, non-generating graph $\Xi(G)$ of $G$ has vertex set $G \setminus Z(G)$, with vertices $x$ and $y$ adjacent whenever $[x,y] \ne 1$ and $\langle x, y \rangle \
Externí odkaz:
http://arxiv.org/abs/2211.08869
Publikováno v:
Internat. J. Algebra Comput. 33 (2023), 509-545
We say that a finite group $G$ satisfies the independence property if, for every pair of distinct elements $x$ and $y$ of $G$, either $\{x,y\}$ is contained in a minimal generating set for $G$ or one of $x$ and $y$ is a power of the other. We give a
Externí odkaz:
http://arxiv.org/abs/2208.04064
Publikováno v:
Monatsh. Math. 203 (2024), 323-340
For a positive integer $k$, a group $G$ is said to be totally $k$-closed if for each set $\Omega$ upon which $G$ acts faithfully, $G$ is the largest subgroup of $\mathrm{Sym}(\Omega)$ that leaves invariant each of the $G$-orbits in the induced action
Externí odkaz:
http://arxiv.org/abs/2206.02347
Publikováno v:
J. Algebraic Combin. 57 (2023), 515-524
A graph is called odd if there is an orientation of its edges and an automorphism that reverses the sense of an odd number of its edges, and even otherwise. Pontus von Br\"omssen (n\'e Andersson) showed that the existence of such an automorphism is i
Externí odkaz:
http://arxiv.org/abs/2204.01947
Autor:
Freedman, Saul D.
Publikováno v:
Arch. Math. (Basel) 117(1) (2021), 1-7
Let $G$ be a non-abelian finite simple group. In addition, let $\Delta_G$ be the intersection graph of $G$, whose vertices are the proper nontrivial subgroups of $G$, with distinct subgroups joined by an edge if and only if they intersect nontriviall
Externí odkaz:
http://arxiv.org/abs/2009.02884
Publikováno v:
Electron. J. Combin., 28(1) (2021), Paper No. 1.16
For a nilpotent group $G$, let $\Xi(G)$ be the difference between the complement of the generating graph of $G$ and the commuting graph of $G$, with vertices corresponding to central elements of $G$ removed. That is, $\Xi(G)$ has vertex set $G \setmi
Externí odkaz:
http://arxiv.org/abs/2008.09291
Autor:
Freedman, Saul D.
Publikováno v:
Comm. Algebra 48 (2020), 4281-4319
Let $\hat G$ be the finite simply connected version of an exceptional Chevalley group, and let $V$ be a nontrivial irreducible module, of minimal dimension, for $\hat G$ over its field of definition. We explore the overgroup structure of $\hat G$ in
Externí odkaz:
http://arxiv.org/abs/1810.08365