共查询到20条相似文献,搜索用时 31 毫秒
1.
Hung P. Tong-Viet 《Monatshefte für Mathematik》2012,15(2):559-577
Let G be a finite group. Denote by Irr(G) the set of all irreducible complex characters of G. Let cd(G)={c(1) | c ? Irr(G)}{{\rm cd}(G)=\{\chi(1)\;|\;\chi\in {\rm Irr}(G)\}} be the set of all irreducible complex character degrees of G forgetting multiplicities, and let X1(G) be the set of all irreducible complex character degrees of G counting multiplicities. Let H be any non-abelian simple exceptional group of Lie type. In this paper, we will show that if S is a non-abelian simple group and cd(S) í cd(H){{\rm cd}(S)\subseteq {\rm cd}(H)} then S must be isomorphic to H. As a consequence, we show that if G is a finite group with X1(G) í X1(H){{\rm X}_1(G)\subseteq {\rm X}_1(H)} then G is isomorphic to H. In particular, this implies that the simple exceptional groups of Lie type are uniquely determined by the structure of their complex group algebras. 相似文献
2.
Timothy J. Ford 《代数通讯》2013,41(9):3277-3298
We study algebra classes and divisor classes on a normal affine surface of the form z 2 = f(x, y). The affine coordinate ring is T = k[x, y, z]/(z 2 ? f), and if R = k[x, y][f ?1] and S = R[z]/(z 2 ? f), then S is a quadratic Galois extension of R. If the Galois group is G, we show that the natural map H1(G, Cl(T)) → H1(G, Pic(S)) factors through the relative Brauer group B(S/R) and that all of the maps are onto. Sufficient conditions are given for H1(G, Cl(T)) to be isomorphic to B(S/R). The groups and maps are computed for several examples. 相似文献
3.
Árpád Tóth 《manuscripta mathematica》2005,116(3):277-295
For a simple Chevalley group G an explicit version of the Solomon-Tits theorem is proved by describing the generators of the kernel of the map Z[G(K)]SK, where K is any field and where SK is the Steinberg module of the group G(K). As a corollary it is shown that if is a Euclidean domain whose fraction field is K, then SK is cyclic as a G() module when G is either a classical group or an exceptional group of type E6, or E7.Acknowledgement I would like to thank Matt Emerton, Özlem Imamoglu, Paul Gunnells for several helpful comments. 相似文献
4.
《代数通讯》2013,41(5):2019-2027
Abstract A subgroup of a group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be S-quasinormally embedded in G if every Sylow subgroup of H is a Sylow subgroup of some S-quasinormal subgroup of G. In this paper we examine the structure of a finite group G under the assumption that certain abelian subgroups of prime power order are S-quasinormally embedded in G. Our results improve and extend recent results of Ramadan [Ramadan, M. (2001). The influence of S-quasinormality of some subgroups of prime power order on the structure of finite groups. Arch. Math. 77:143–148]. 相似文献
5.
《代数通讯》2013,41(3):1201-1211
Abstract For a group G and a subset S of G which does not contain the identity of G, the Cayley digraph Cay(G, S) is called normal if R(G) is normal in Aut(Γ). In this paper, we investigate the normality of Cayley digraphs of finite simple groups with out-valency 2 and 3. We give several sufficient conditions for such Cayley digraphs to be normal. By using this result, we consider the digraphical regular representations of finite simple groups. 相似文献
6.
《代数通讯》2013,41(5):1289-1302
ABSTRACT Let x be a p-element of a finite group G. We say that x is unfused in G if, for some Sylow p-subgroup S of G containing x, all G-conjugates of x in S are S-conjugates. It is shown (using the classification of finite simple groups) that a finite group that contains an unfused involution has a chief factor of order 2. 相似文献
7.
Let π(G,A):IrrA(G)→Irr(CG(A)) be the Glauberman–Isaacs correspondence, where G and A are finite groups with coprime orders and A acts on G by automorphisms. Let B be a subgroup of A. In this setting, we give some new conditions for the fixed-point subgroups CG(A) and CG(B) such that χπ(G,A) is an irreducible constituent of the restriction of χπ(G,B) to CG(A) for all χIrrA(G). 相似文献
8.
Thomas Michael Keller 《Israel Journal of Mathematics》2009,171(1):367-384
Let G be a finite group and V be a finite G-module. We present upper bounds for the cardinalities of certain subsets of Irr(GV), such as the set of those χ ∈ Irr(GV) such that, for a fixed v ∈ V, the restriction of χ to 〈v〉 is not a multiple of the regular character of 〈v〉. These results might be useful in attacking the noncoprime k(GV)-problem. 相似文献
9.
Mark L. Lewis 《代数通讯》2013,41(4):1273-1292
A finite group G is odd-square-free if no irreducible complex character of G has degree divisible by the square of an odd prime. We determine all odd-square-free groups G satisfying S ≤ G ≤ Aut(S) for a finite simple group S. More generally, we show that if G is any nonsolvable odd-square-free group, then G has at most two nonabelian chief factors and these must be simple odd-square-free groups. If the alternating group A 7 is involved in G, the structure of G can be further restricted. 相似文献
10.
Alexandre Turull 《Advances in Mathematics》2008,217(5):2170-2205
Let S be a finite solvable group, and suppose S acts on the finite group N, and they have coprime orders. Then, the celebrated Glauberman correspondence provides a natural bijection from the set IrrS(N) of irreducible characters of N which are invariant under the action of S to the set Irr(CN(S)) of all irreducible characters of the centralizer of S in N. Suppose, further, that the semidirect product SN is a normal subgroup of a finite group G. Let θ∈IrrS(N), and let ψ∈Irr(CN(S)) be its Glauberman correspondent. We prove that there is a bijection with good compatibility properties from the set Irr(G,θ) of the irreducible characters of G above θ to Irr(NG(S),ψ) such that, in the case when S is a p-group for some prime p, it preserves fields of values and Schur indices over Qp, the field of p-adic numbers. Using this result, we also prove a strengthening of the McKay Conjecture for all p-solvable groups. 相似文献
11.
Jinfeng Feng 《Mathematical Methods of Operations Research》2009,69(2):343-352
Let G = (V, E) be a connected graph. For a vertex subset , G[S] is the subgraph of G induced by S. A cycle C (a path, respectively) is said to be an induced cycle (path, respectively) if G[V(C)] = C (G[V(P)] = P, respectively). The distance between a vertex x and a subgraph H of G is denoted by , where d(x, y) is the distance between x and y. A subgraph H of G is called 2-dominating if d(x, H) ≤ 2 for all . An induced path P of G is said to be maximal if there is no induced path P′ satisfying and . In this paper, we assume that G is a connected claw-free graph satisfying the following condition: for every maximal induced path P of length p ≥ 2 with end vertices u, v it holds:
Under this assumption, we prove that G has a 2-dominating induced cycle and G is Hamiltonian.
J. Feng is an associate member of “Graduiertenkolleg: Hierarchie und Symmetrie in mathematischen Modellen (DFG)” at RWTH Aachen,
Germany. 相似文献
12.
Martín Matamala 《Journal of Graph Theory》2007,55(3):227-232
Let G be a graph with maximum degree d≥ 3 and ω(G)≤ d, where ω(G) is the clique number of the graph G. Let p1 and p2 be two positive integers such that d = p1 + p2. In this work, we prove that G has a vertex partition S1, S2 such that G[S1] is a maximum order (p1‐1)‐degenerate subgraph of G and G[S2] is a (p2‐1)‐degenerate subgraph, where G[Si] denotes the graph induced by the set Si in G, for i = 1,2. On one hand, by using a degree‐equilibrating process our result implies a result of Bollobas and Marvel [ 1 ]: for every graph G of maximum degree d≥ 3 and ω(G)≤ d, and for every p1 and p2 positive integers such that d = p1 + p2, the graph G has a partition S1,S2 such that for i = 1,2, Δ(G[Si])≤ pi and G[Si] is (pi‐1)‐degenerate. On the other hand, our result refines the following result of Catlin in [ 2 ]: every graph G of maximum degree d≥ 3 has a partition S1,S2 such that S1 is a maximum independent set and ω(G[S2])≤ d‐1; it also refines a result of Catlin and Lai [ 3 ]: every graph G of maximum degree d≥ 3 has a partition S1,S2 such that S1 is a maximum size set with G[S1] acyclic and ω(G[S2])≤ d‐2. The cases d = 3, (d,p1) = (4,1) and (d,p1) = (4,2) were proved by Catlin and Lai [ 3 ]. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 227–232, 2007 相似文献
13.
F. E. A. Johnson 《K-Theory》2005,34(2):141-150
In [F.E.A. Johnson, Stable Modules and the D(2)-Problem, LMS Lecture Notes In Mathematics, vol. 301, CUP (2003)], for finite groups G, we gave a parametrization of the stable class of the augmentation ideal of Z[G] in terms of stably free modules. Whilst the details of this parametrization break down immediately for infinite groups,
nevertheless one may hope to find parallel arguments for restricted classes of infinite groups. Subject to the restriction
that Ext1(Z, Z[G]) = 0, we parametrize the minimal level in Ω1(Z) by means of stably free modules and give a lower estimate for the size of Ω1(Z). 相似文献
14.
Bangming Deng 《代数通讯》2013,41(10):3419-3434
Let G be a group and let N be a normal subgroup of G. We set cd(G|N) to be the degrees of the irreducible characters of G whose kernels do not contain N. We associate a graph with this set. The vertices of this graph are the primes dividing degrees in cd(G|N), and there is an edge between p and q if pq divides some degree in cd(G|N). In this paper, we study this graph when it is disconnected, and we study its diameter when it is connected. 相似文献
15.
For two vertices u and v of a connected graph G, the set I[u,v] consists of all those vertices lying on a u−v shortest path in G, while for a set S of vertices of G, the set I[S] is the union of all sets I[u,v] for u,v∈S. A set S is convex if I[S]=S. The convexity number con(G) of G is the maximum cardinality of a proper convex set of G. The clique number ω(G) is the maximum cardinality of a clique in G. If G is a connected graph of order n that is not complete, then n≥3 and 2≤ω(G)≤con(G)≤n−1. It is shown that for every triple l,k,n of integers with n≥3 and 2≤l≤k≤n−1, there exists a noncomplete connected graph G of order n with ω(G)=l and con(G)=k. Other results on convex numbers are also presented.
Received: August 19, 1998 Final version received: May 17, 2000 相似文献
16.
In this article we prove that if S is a faithfully projective R-algebra and H is a finite inverse semigroup acting on S as R-linear maps such that the fixed subring S H = R, then any partial isomorphism between ideals of S which are generated by central idempotents can be obtained as restriction of an R-automorphism of S and there exists a finite subgroup of automorphisms G of S with S G = R. 相似文献
17.
A character pair (H, ) in a group G is a subgroup H and a character Irr(H). Following Dade, we say that a character pair (H, ) is an inductive source in G if induction to G defines an injective map from the irreducible characters of the stabilizer of (H, ) that lie over into Irr(G). (By the Clifford correspondence, this necessarily happens if H is normal in G.) A character pair is said to be conjugate stable if its conjugates satisfy a certain technical condition. We show that an inductive source must be conjugate stable and we present an example of a character pair that is conjugate stable but is not an inductive source. Finally, if (H, ) is conjugate stable and H is a subnormal subgroup of G, we show that (H, ) must be an inductive source in G. 相似文献
18.
《代数通讯》2013,41(9):3641-3649
Abstract Let G be a finite group and let cd(G) be the set of irreducible character degrees of G. The degree graph Δ(G) of G is the graph whose set of vertices is the set of primes that divide degrees in cd(G), with an edge between p and q if pq divides a for some degree a ∈ cd(G). In this paper, we determine the graph Δ(G) when G is a finite simple group of exceptional Lie type. 相似文献
19.
《代数通讯》2013,41(7):2109-2114
ABSTRACT If M is a simple module over a ring R, then, by Schur's Lemma, its endomorphism ring is a division ring. However, the converse of this property, which we called the CSL property, does not hold in general. The object of this article is to study this converse for a few classes of rings: left Noetherian rings, V-rings and group algebras. First, we establish that a left Noetherian ring R is a CSL ring if and only if a ring R is left–artinian and primary decomposable. Secondly, we prove that a left semiartinian V-ring is CSL. At last, we study the CSL property in group algebra K [ G ] where K a field algebraically closed of characteristic p and G is a finite group of order divisible by p. Our main contribution is that K [ G ] is a CSL ring if and only if Gbf = HP where H is a normal p′-subgroup and bfP a Sylow bfp-subgroup of bfG. In this case, K [ G ] is primary decomposable. 相似文献
20.
Let G be a nonabelian finite group. Then Irr(G/G′) is an abelian group under the multiplication of characters and acts on the set of non-linear irreducible characters of G via the multiplication of characters. The purpose of this paper is to establish some facts about the action of linear character group on non-linear irreducible characters and determine the structures of groups G for which either all the orbit kernels are trivial or the number of orbits is at most two. Using the established results on this action, it is very easy to classify groups G having at most three nomlinear irreducible characters. 相似文献