共查询到20条相似文献,搜索用时 31 毫秒
1.
Suppose that V is a finite faithful irreducible G-module where G is a finite solvable group of odd order. We prove if the action is quasi-primitive, then either F(G) is abelian or G has at least 212 regular orbits on V. As an application, we prove that when V is a finite faithful completely reducible G-module for a solvable group G of odd order, then there exists v ∈ V such that C G (v) ? F 2(G) (where F 2(G) is the 2nd ascending Fitting subgroup of G). We also generalize a result of Espuelas and Navarro. Let G be a group of odd order and let H be a Hall π-subgroup of G. Let V be a faithful G-module over a finite field of characteristic 2, then there exists v ∈ V such that C H (v) ? O π(G). 相似文献
2.
《代数通讯》2013,41(11):4495-4505
Résumé On donne une réponse explicite à la question suivante: étant donné un 3-cocycle Φ (sur le groupe G = ? N , à valeurs dans le G-module trivial ?) dont l'antisymétrisé est nul, construire une 2-cochaîne admettant Φ comme cobord. Abstract We give an explicit answer to the following question: given a 3-cocycle Φ (on the group G = ? N , with values in the trivial G-module ?) whose antisymmetric part is zero, construct a 2-cochain having Φ as coboundary. 相似文献
3.
We show that an iteration of the procedure used to define the Gorenstein projective modules over a ring R yields exactly the Gorenstein projective modules. Specifically, given an exact sequence of Gorenstein projective left R-modules G = … → G 1 → G 0 → G 0 → G 1 → … such that the complex Hom R (G, H) is exact for each projective left R-module H, the module Im(G 0 → G 0) is Gorenstein projective. We also get similar results for Gorenstein flat left R-modules when R is a right coherent ring. As applications, we obtain the corresponding results for Gorenstein complexes. 相似文献
4.
James E. Arnold 《代数通讯》2013,41(2):599-614
Abstract Let R be a commutative Noetherian local Gorenstein ring with residue field k. We show that G(k), the Gorenstein injective envelope of k, is an artinian R-module, and we compute G(k) in the case where R = k[[S]] is a semigroup ring and S is symmetric. We also show that a certain subring of the endomorphism ring of G(k) is a complete local (but possibly non-commutative) ring. 相似文献
5.
A ring R is called left P-coherent in case each principal left ideal of R is finitely presented. A left R-module M (resp. right R-module N) is called D-injective (resp. D-flat) if Ext1(G, M) = 0 (resp. Tor1(N, G) = 0) for every divisible left R-module G. It is shown that every left R-module over a left P-coherent ring R has a divisible cover; a left R-module M is D-injective if and only if M is the kernel of a divisible precover A → B with A injective; a finitely presented right R-module L over a left P-coherent ring R is D-flat if and only if L is the cokernel of a torsionfree preenvelope K → F with F flat. We also study the divisible and torsionfree dimensions of modules and rings. As applications, some new characterizations of von Neumann regular rings and PP rings are given. 相似文献
6.
7.
Dessislava H. Kochloukova 《代数通讯》2013,41(1):253-259
Let G be a finitely generated group, and A a ?[G]-module of flat dimension n such that the homological invariant Σ n (G, A) is not empty. We show that A has projective dimension n as a ?[G]-module. In particular, if G is a group of homological dimension hd(G) = n such that the homological invariant Σ n (G, ?) is not empty, then G has cohomological dimension cd(G) = n. We show that if G is a finitely generated soluble group, the converse is true subject to taking a subgroup of finite index, i.e., the equality cd (G) = hd(G) implies that there is a subgroup H of finite index in G such that Σ∞(H, ?) ≠ ?. 相似文献
8.
Pablo Spiga 《代数通讯》2013,41(7):2540-2545
Let K be a field of characteristic p > 0, K* the multiplicative group of K and G = G p × B a finite group, where G p is a p-group and B is a p′-group. Denote by K λ G a twisted group algebra of G over K with a 2-cocycle λ ∈Z 2(G, K*). In this article, we give necessary and sufficient conditions for K λ G to be of OTP representation type, in the sense that every indecomposable K λ G-module is isomorphic to the outer tensor product V#W of an indecomposable K λ G p -module V and an irreducible K λ B-module W. 相似文献
9.
10.
Massoud Tousi 《代数通讯》2013,41(11):3977-3987
ABSTRACT Assume that ?:(R, ± 𝔪) → (S, ± 𝔫) is a local flat homomorphism between commutative Noetherian local rings R and S. Let M be a finitely generated R-module. We investigate the ascent and descent of sequentially Cohen-Macaulay properties between the R-module M and the S-module M ? R S. 相似文献
11.
David I. Stewart 《代数通讯》2013,41(12):4702-4716
Let G be the simple, simply connected algebraic group SL 3 defined over an algebraically closed field K of characteristic p > 0. In this article, we find H 2(G, V) for any irreducible G-module V. When p > 7, we also find H 2(G(q), V) for any irreducible G(q)-module V for the finite Chevalley groups G(q) = SL(3, q) where q is a power of p. 相似文献
12.
For any group G such that G is a right R-module for some ring R, the elements of R act on G as endomorphisms and we obtain the near-ring of R-homogeneous maps on G: MR(G) = {f: G → G|f(ga) = f(g)a for all a ∈ R, g ∈ G}. In the special case that R is a topological ring and G is a topological R-module, we study NR(G): = {f ∈ MR(G)|f is continuous}. In particular, we investigate primeness of the near-ring NR(G) of continuous homogeneous maps on G. 相似文献
13.
Let R be a commutative ring with unit, and let E be an R-module. We say the functor of R-modules E, defined by E(B) = E ? R B, is a quasi-coherent R-module, and its dual E* is an R-module scheme. Both types of R-module functors are essential for the development of the theory of the linear representations of an affine R-group. We prove that a quasi-coherent R-module E is an R-module scheme if and only if E is a projective R-module of finite type, and, as a consequence, we also characterize finitely generated projective R-modules. 相似文献
14.
In this article, we study the weak global dimension of coherent rings in terms of the left FP-injective resolutions of modules. Let R be a left coherent ring and ? ? the class of all FP-injective left R-modules. It is shown that wD(R) ≤ n (n ≥ 1) if and only if every nth ? ?-syzygy of a left R-module is FP-injective; and wD(R) ≤ n (n ≥ 2) if and only if every (n ? 2)th ? ?-syzygy in a minimal ? ?-resolution of a left R-module has an FP-injective cover with the unique mapping property. Some results for the weak global dimension of commutative coherent rings are also given. 相似文献
15.
Olga Yu. Dashkova 《Central European Journal of Mathematics》2011,9(4):922-928
Let A be an R
G-module, where R is an integral domain and G is a soluble group. Suppose that C
G
(A) = 1 and A/C
A
(G) is not a noetherian R-module. Let L
nnd(G) be the family of all subgroups H of G such that A/C
A
(H) is not a noetherian R-module. In this paper we study the structure of those G for which L
nnd(G) satisfies the maximal condition. 相似文献
16.
O. Yu. Dashkova 《Journal of Mathematical Sciences》2010,169(5):636-643
We consider an R
G-module A over a commutative Noetherian ring R. Let G be a group having infinite section p-rank (or infinite 0-rank) such that C
G
(A) = 1, A/C
A
(G) is not a Noetherian R-module, but the quotient A/C
A
(H) is a Noetherian R-module for every proper subgroup H of infinite section p-rank (or infinite 0-rank, respectively). In this paper, it is proved that if G is a locally soluble group, then G is soluble. Some properties of soluble groups of this type are also obtained. 相似文献
17.
Lingli Wang 《代数通讯》2013,41(2):523-528
Let G be a nonabelian group and associate a noncommuting graph ?(G) with G as follows: The vertex set of ?(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. In 1987, Professor J. G. Thompson gave the following conjecture. Thompson's Conjecture. If G is a finite group with Z(G) = 1 and M is a nonabelian simple group satisfying N(G) = N(M), then G ? M, where N(G):={n ∈ ? | G has a conjugacy class of size n}. In 2006, A. Abdollahi, S. Akbari, and H. R. Maimani put forward a conjecture (AAM's conjecture) in Abdollahi et al. (2006) as follows. AAM's Conjecture. Let M be a finite nonabelian simple group and G a group such that ?(G) ? ? (M). Then G ? M. In this short article we prove that if G is a finite group with ?(G) ? ? (A 10), then G ? A 10, where A 10 is the alternating group of degree 10. 相似文献
18.
《代数通讯》2013,41(4):1777-1797
Abstract In this paper we introduce and study the local quiver as a tool to investigate the étale local structure of moduli spaces of θ-semistable representations of quivers. As an application we determine the dimension vectors associated to irreducible representations of the torus knot groups G p,q = ?a, b ∣ a p = b q ?. 相似文献
19.
Willian Franca 《代数通讯》2013,41(6):2621-2634
Let R be a simple unital ring. Under a mild technical restriction on R, we will characterize biadditive mappings G: R2 → R satisfying G(u, u)u = uG(u, u), and G(1, r) = G(r, 1) = r for all unit u ∈ R and r ∈ R, respectively. As an application, we describe bijective linear maps θ: R → R satisfying θ(xyx?1y?1) = θ(x)θ(y)θ(x)?1θ(y)?1 for all invertible x, y ∈ R. This solves an open problem of Herstein on multiplicative commutators. More precisely, we will show that θ is an isomorphism. Furthermore, we shall see the existence of a unital simple ring R′ without nontrivial idempotents, that admits a bijective linear map f: R′ → R′, preserving multiplicative commutators, that is not an isomorphism. 相似文献
20.
《代数通讯》2013,41(11):4507-4513
Abstract Let G be a finite group and ω(G) the set of all orders of elements in G. Denote by h(ω(G)) the number of isomorphism classes of finite groups H satisfying ω(H) = ω(G), and put h(G) = h(ω(G)). A group G is called k-recognizable if h(G) = k < ∞ , otherwise G is called non-recognizable. In the present article we will show that the simple groups PSL(3, q), where q ≡ ±2(mod 5) and (6, (q ? 1)/2) = 2, are 2-recognizable. Therefore if q is a prime power and q ≡ 17, 33, 53 or 57 (mod 60), then the groups PSL(3, q) are 2-recognizable. Hence proving the existing of an infinite families of 2-recognizable simple groups. 相似文献