共查询到20条相似文献,搜索用时 31 毫秒
1.
B KRISHNAKUMARI Y B VENKATAKRISHNAN MARCIN KRZYWKOWSKI 《Proceedings Mathematical Sciences》2016,126(2):153-157
An edge e∈E(G) dominates a vertex v∈V(G) if e is incident with v or e is incident with a vertex adjacent to v. An edge-vertex dominating set of a graph G is a set D of edges of G such that every vertex of G is edge-vertex dominated by an edge of D. The edge-vertex domination number of a graph G is the minimum cardinality of an edge-vertex dominating set of G. A subset D?V(G) is a total dominating set of G if every vertex of G has a neighbor in D. The total domination number of G is the minimum cardinality of a total dominating set of G. We characterize all trees with total domination number equal to edge-vertex domination number plus one. 相似文献
2.
Let G be a p-nilpotent linear group on a finite vector space V of characteristic p. Suppose that |G||V| is odd. Let P be a Sylow p-subgroup of G. We show that there exist vectors \(v_1\) and \(v_2\) in V such that \(C_G(v_1) \cap C_G(v_2)=P\). A striking conjecture of Malle and Navarro offers a simple global criterion for the nilpotence (in the sense of Broué and Puig) of a p-block of a finite group. Our result implies that this conjecture holds for groups of odd order. 相似文献
3.
A total weighting of a graph G is a mapping ? that assigns to each element z ∈ V (G)∪E(G) a weight ?(z). A total weighting ? is proper if for any two adjacent vertices u and v, ∑ e∈E(u) ?(e)+?(u)≠∑ e∈E(v) ?(e)+?(v). This paper proves that if each edge e is given a set L(e) of 3 permissible weights, and each vertex v is given a set L(v) of 2 permissible weights, then G has a proper total weighting ? with ?(z) ∈ L(z) for each element z ∈ V (G)∪E(G). 相似文献
4.
Let G be a finite group and k a field of characteristic p > 0. In this paper, we obtain several equivalent conditions to determine whether the principal block B0 of a finite p-solvable group G is p-radical, which means that B0 has the property that e0(kP)G is semisimple as a kG-module, where P is a Sylow p-subgroup of G, kP is the trivial kP-module, (kP)G is the induced module, and e0 is the block idempotent of B0. We also give the complete classification of a finite p-solvable group G which has not more than three simple B0-modules where B0 is p-radical. 相似文献
5.
Nguyen Ngoc Hung Mark L. Lewis Amanda A. Schaeffer Fry 《manuscripta mathematica》2016,149(3-4):523-546
Let G be a finite group and d the degree of a complex irreducible character of G, then write |G| = d(d + e) where e is a nonnegative integer. We prove that |G| ≤ e4?e3 whenever e > 1. This bound is best possible and improves on several earlier related results. 相似文献
6.
Let G be a finite group and e a positive integer dividing |G|, the order of G. Denoting \({L_e(G)=\{x\in G|\,x^e=1\}}\) , Frobenius proved that |L e (G)| = ke for a positive integer k ≥ 1. In this paper, we give a complete classification of finite groups G with |L e (G)| ≤ 2e for every e dividing |G|. 相似文献
7.
Let G be a finite group, and let V be a completely reducible faithful Gmodule. It has been known for a long time that if G is abelian, then G has a regular orbit on V. In this paper we generalize this result as follows. Assuming G to be solvable, we show that G has an orbit of size at least |G/G′| on V. This also strengthens a result of Aschbacher and Guralnick in that situation. Additionally, we prove a similar generalization of the well-known result that if G is nilpotent, then G has an orbit of size at least \(\sqrt {\left| G \right|} \) on V. 相似文献
8.
Let G be a simple algebraic group of type G2 over an algebraically closed field of characteristic 2. We give an example of a finite group Γ with Sylow 2-subgroup Γ2 and an infinite family of pairwise non-conjugate homomorphisms ρ: Γ → G whose restrictions to Γ2 are all conjugate. This answers a question of Burkhard Külshammer from 1995. We also give an action of Γ on a connected unipotent group V such that the map of 1-cohomologies H1(Γ, V) → H1(Γp, V) induced by restriction of 1-cocycles has an infinite fibre. 相似文献
10.
Benjamin Klopsch 《Archiv der Mathematik》2011,96(4):321-333
The rank of a profinite group G is the basic invariant \({{\rm rk}(G):={\rm sup}\{d(H) \mid H \leq G\}}\), where H ranges over all closed subgroups of G and d(H) denotes the minimal cardinality of a topological generating set for H. A compact topological group G admits the structure of a p-adic Lie group if and only if it contains an open pro-p subgroup of finite rank. For every compact p-adic Lie group G one has rk(G) ≥ dim(G), where dim(G) denotes the dimension of G as a p-adic manifold. In this paper we consider the converse problem, bounding rk(G) in terms of dim(G). Every profinite group G of finite rank admits a maximal finite normal subgroup, its periodic radical π(G). One of our main results is the following. Let G be a compact p-adic Lie group such that π(G) = 1, and suppose that p is odd. If \(\{g \in G \mid g^{p-1}=1 \}\) is equal to {1}, then rk(G) = dim(G). 相似文献
11.
We show that if for every prime p, the normalizer of a Sylow p-subgroup of a finite group G admits a p-solvable supplement, then G is solvable. This generalizes a solvability criterion of Hall which asserts that a finite group G is solvable if and only if G has a Hall p′-subgroup for every prime p. 相似文献
12.
We give a simple sufficient condition for a weighted graph to have a diameter-preserving spanning tree. More precisely, let G = (V, E, f E ) be a connected edge weighted graph with f E being the edge weight function. Let f V be the vertex weight function of G induced by f E as follows: f V (v) = max{f E (e) : e is incident with v} for all \({v \in V}\) . We show that G contains a diameter-preserving spanning tree if \({d(G)\ge \frac{2}{3} \sum_{v\in V} f_V(v)}\) where d(G) is the diameter of G. The condition is sharp in the sense that for any \({\epsilon >0 }\) , there exist weighted graphs G satisfying \({d(G) > (\frac{2}{3}-\epsilon)\sum_{v\in V} f_V(v)}\) and not containing a diameter-preserving spanning tree. 相似文献
13.
Let G be a finite group, let p be a prime, and let P be a Sylow p-subgroup of G. In this note we give a cohomological criterion for the p-solvability of G depending on the cohomology in degree 1 with coefficients in \(\mathbb F_p\) of both the normal subgroups of G and P. As a byproduct we bound the minimum possible number of factors of p-power order appearing in any normal series of G, in which each factor is either a p-group, a p’-group, or a non-p-solvable characteristically simple group, by the number of generators of P. 相似文献
14.
Lijian An 《Frontiers of Mathematics in China》2018,13(4):763-777
Suppose that G is a finite p-group. If G is not a Dedekind group, then G has a non-normal subgroup. We use pM(G) and pm(G) to denote the maximum and minimum of the orders of the non-normal subgroups of G; respectively. In this paper, we classify groups G such that M(G) < 2m(G)?1: As a by-product, we also classify p-groups whose orders of non-normal subgroups are pk and pk+1. 相似文献
15.
Let G be a finite group, and let N(G) be the set of conjugacy class sizes of G. By Thompson’s conjecture, if L is a finite non-abelian simple group, G is a finite group with a trivial center, and N(G) = N(L), then L and G are isomorphic. Recently, Chen et al. contributed interestingly to Thompson’s conjecture under a weak condition. They only used the group order and one or two special conjugacy class sizes of simple groups and characterized successfully sporadic simple groups (see Li’s PhD dissertation). In this article, we investigate validity of Thompson’s conjecture under a weak condition for the alternating groups of degrees p+1 and p+2, where p is a prime number. This work implies that Thompson’s conjecture holds for the alternating groups of degree p + 1 and p + 2. 相似文献
16.
Hamiltonian cycles in Dirac graphs 总被引:1,自引:1,他引:0
We prove that for any n-vertex Dirac graph (graph with minimum degree at least n/2) G=(V,E), the number, Ψ(G), of Hamiltonian cycles in G is at least where h(G)=maxΣ e x e log(1/x e ), the maximum over x: E → ?+ satisfying Σ e?υ x e = 1 for each υ ∈ V, and log =log2. (A second paper will show that this bound is tight up to the o(n).)
We also show that for any (Dirac) G of minimum degree at least d, h(G) ≥ (n/2) logd, so that Ψ(G) > (d/(e + o(1))) n . In particular, this says that for any Dirac G we have Ψ(G) > n!/(2 + o(1)) n , confirming a conjecture of G. Sárközy, Selkow, and Szemerédi which was the original motivation for this work. 相似文献
$exp_2 [2h(G) - n\log e - o(n)],$
17.
On <Emphasis Type="Italic">c</Emphasis><Superscript>#</Superscript>-normal subgroups infinite groups
Huaquan Wei Qiao Dai Hualian Zhang Yubo Lv Liying Yang 《Frontiers of Mathematics in China》2018,13(5):1169-1178
A subgroup H of a finite group G is called a c#-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H ∩ K is a CAP-subgroup of G: In this paper, we investigate the influence of fewer c#-normal subgroups of Sylow p-subgroups on the p-supersolvability, p-nilpotency, and supersolvability of finite groups. We obtain some new sufficient and necessary conditions for a group to be p-supersolvable, p-nilpotent, and supersolvable. Our results improve and extend many known results. 相似文献
18.
We continue the study of glider representations of finite groups G with given structure chain of subgroups e ? G 1 ?… ? G d = G. We give a characterization of irreducible gliders of essential length e ≤ d which in the case of p-groups allows to prove some results about classical representation theory. The paper also contains an introduction to generalized character theory for glider representations and an extension of the decomposition groups in the Clifford theory. Furthermore, we study irreducible glider representations for products of groups and nilpotent groups. 相似文献
19.
For a finite group G denote by N(G) the set of conjugacy class sizes of G. In 1980s, J.G.Thompson posed the following conjecture: If L is a finite nonabelian simple group, G is a finite group with trivial center and N(G) = N(L), then G ? L. We prove this conjecture for an infinite class of simple groups. Let p be an odd prime. We show that every finite group G with the property Z(G) = 1 and N(G) = N(A i ) is necessarily isomorphic to A i , where i ∈ {2p, 2p + 1}. 相似文献
20.
Let G be a graph and k ≥ 2 a positive integer. Let h: E(G) → [0, 1] be a function. If \(\sum\limits_{e \mathrel\backepsilon x} {h(e) = k} \) holds for each x ∈ V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e ∈ E(G): h(e) > 0}. A graph G is fractional independent-set-deletable k-factor-critical (in short, fractional ID-k-factor-critical), if G ? I has a fractional k-factor for every independent set I of G. In this paper, we prove that if n ≥ 9k ? 14 and for any subset X ? V (G) we have then G is fractional ID-k-factor-critical.
相似文献
$${N_G}(X) = V(G)if|X| \geqslant \left\lfloor {\frac{{kn}}{{3k - 1}}} \right\rfloor ;or|{N_G}(X)| \geqslant \frac{{3k - 1}}{k}|X|if|X| < \left\lfloor {\frac{{kn}}{{3k - 1}}} \right\rfloor ,$$