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1.
If V is a (possibly infinite) set, G a permutation group on ${V, v\in V}$ , and Ω is an orbit of the stabiliser G v , let ${G_v^{\Omega}}$ denote the permutation group induced by the action of G v on Ω, and let N be the normaliser of G in Sym(V). In this article, we discuss a relationship between the structures of G v and ${G_v^\Omega}$ . If G is primitive and G v is finite, then by a theorem of Betten et?al. (J Group Theory 6:415–420, 2003) we can conclude that every composition factor of the group G v is also a composition factor of the group ${G_v^{\Omega(v)}}$ . In this paper we generalize this result to possibly imprimitive permutation groups G with infinite vertex-stabilisers, subject to certain restrictions that can be expressed in terms of the natural permutation topology on Sym(V). In particular, we show the following: If ${\Omega=u^{G_v}}$ is a suborbit of a transitive closed subgroup G of Sym(V) with a normalizing overgroup N?≤ N Sym(V)(G) such that the N-orbital ${\{(v^g,u^g) \mid u\in \Omega, g\in N\}}$ is locally finite and strongly connected (when viewed as a digraph on V), then every closed simple section of G v is also a section of ${G_v^\Omega}$ . To demonstrate that the topological assumptions on G and the simple sections of G v cannot be omitted in this statement, we give an example of a group G acting arc-transitively on an infinite cubic tree, such that the vertex-stabiliser G v is isomorphic to the modular group ${{\rm PSL}(2,\mathbb{Z}) \cong C_2*C_3}$ , which is known to have infinitely many finite simple groups among its sections. 相似文献
2.
Let
W ì \BbbR2\Omega \subset \Bbb{R}^2 denote a bounded domain whose boundary
?W\partial \Omega is Lipschitz and contains a segment G0\Gamma_0 representing
the austenite-twinned martensite interface. We prove
infu ? W(W) òW j(?u(x,y))dxdy=0\displaystyle{\inf_{{u\in \cal W}(\Omega)} \int_\Omega \varphi(\nabla
u(x,y))dxdy=0} 相似文献
3.
Given a graph G = (V, E), a set W í V{W \subseteq V} is said to be a resolving set if for each pair of distinct vertices u, v ? V{u, v \in V} there is a vertex x in W such that d(u, x) 1 d(v, x){d(u, x) \neq d(v, x)} . The resolving number of G is the minimum cardinality of all resolving sets. In this paper, conditions are imposed on resolving sets and certain conditional
resolving parameters are studied for honeycomb and hexagonal networks. 相似文献
4.
For a graph G of order |V(G)| = n and a real-valued mapping
f:V(G)?\mathbbR{f:V(G)\rightarrow\mathbb{R}}, if S ì V(G){S\subset V(G)} then f(S)=?w ? S f(w){f(S)=\sum_{w\in S} f(w)} is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, NS[f]=max{f(N[v])|v ? V(G)}{NS[f]={\rm max}\{f(N[v])|v \in V(G)\}} and NS(f)=max{f(N(v))|v ? V(G)}{NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, NS-[f]=min{f(N[v])|v ? V(G)}{NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}} and NS-(f)=min{f(N(v))|v ? V(G)}{NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}. For
W ì \mathbbR{W\subset \mathbb{R}}, the closed and open neighborhood sum parameters are NSW[G]=min{NS[f]|f:V(G)? W{NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W} is a bijection} and NSW(G)=min{NS(f)|f:V(G)? W{NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W} is a bijection}. The lower neighbor sum parameters are NS-W[G]=maxNS-[f]|f:V(G)? W{NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W} is a bijection} and NS-W(G)=maxNS-(f)|f:V(G)? W{NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W} is a bijection}. For bijections f:V(G)? {1,2,?,n}{f:V(G)\rightarrow \{1,2,\ldots,n\}} we consider the parameters NS[G], NS(G), NS
−[G] and NS
−(G), as well as two parameters minimizing the maximum difference in neighborhood sums. 相似文献
5.
Sami Baraket Ines Ben Omrane Taieb Ouni 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(1):59-78
Given a bounded open regular set
W ì \mathbbR2{\Omega \subset \mathbb{R}^2} and x1, x2, ?, xm ? W{x_1, x_2, \ldots, x_m \in \Omega}, we give a sufficient condition for the problem
-div(a(u)?u) = r2 f(u) -{\rm div}(a(u)\nabla u)= \rho^{2} f(u) 相似文献
6.
Marino Badiale Lorenzo Pisani Sergio Rolando 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(4):369-405
We study the sum of weighted Lebesgue spaces, by considering an abstract measure space (W,A,m){(\Omega ,\mathcal{A},\mu)} and investigating the main properties of both the Banach space
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