共查询到20条相似文献,搜索用时 31 毫秒
1.
Let G be a finite group. A subgroup K of a group G is called an ?-subgroup of G if N G (K) ∩ K x ≦ K for all x ? G. The set of all ?-subgroups of G will be denoted by ?(G). Let P be a nontrivial p-group. A chain of subgroups 1 = P 0 ? P 1 ? ··· ? P n = P is called a maximal chain of P provided that |P i : P i?1| = p, i = 1, 2, ···, n. A nontrivial p-subgroup P of G is called weakly supersolvably embedded in G if P has a maximal chain 1 = P 0 ? P 1 ? ··· ? P i ? ··· ? P n = P such that P i ? ?(G) for i = 1, 2, ···, n. Using the concept of weakly supersolvably embedded, we obtain new characterizations of p-nilpotent and supersolvable finite groups. 相似文献
2.
Let s ∈ {2.3,…} and E be an Archimedean vector lattice. We prove that there exists a unique pair (E ? ,?), where E ? is an Archimedean vector lattice and ?:E× ··· ×E (s times) → E ? is a symmetric lattice s-morphism, such that for every Archimedean vector lattice F and every symmetric lattice s-morphism T:E × ··· × E (s times) → F, there exists a unique lattice homomorphism T ? :E ? → F such that T = T ? ○?. We give two approaches to construct (E ? ,?) based on f-algebras and functional calculus, respectively, provided that E is also uniformly complete. 相似文献
3.
Let A be an abelian group. A group B is A-solvable if the natural map Hom(A, B) ? E(A) A → B is an isomorphism. We study pure subgroups of A-solvable groups for a self-small group A of finite torsion-free rank. Particular attention is given to the case that A is in , the class of self-small mixed groups G with G/tG? ? n for some n < ω. We obtain a new characterization of the elements of , and demonstrate that differs in various ways from the class ? of torsion-free abelian groups of finite rank despite the fact that the quasi-category ? is dual to a full subcategory of ? ?. 相似文献
4.
Robert Wisbauer 《代数通讯》2013,41(7):2683-2711
Generalizing the notion of Galois corings, Galois comodules were introduced as comodules P over an A-coring 𝒞 for which P A is finitely generated and projective and the evaluation map μ𝒞:Hom 𝒞 (P, 𝒞) ? S P → 𝒞 is an isomorphism (of corings) where S = End 𝒞 (P). It has been observed that for such comodules the functors ? ? A 𝒞 and Hom A (P, ?) ? S P from the category of right A-modules to the category of right 𝒞-comodules are isomorphic. In this note we use this isomorphism related to a comodule P to define Galois comodules without requiring P A to be finitely generated and projective. This generalises the old notion with this name but we show that essential properties and relationships are maintained. Galois comodules are close to being generators and have common properties with tilting (co)modules. Some of our results also apply to generalised Hopf Galois (coalgebra Galois) extensions. 相似文献
5.
George Szeto 《代数通讯》2013,41(12):3979-3985
Let B be a Galois algebra over a commutative ring R with Galois group G such that B H is a separable subalgebra of B for each subgroup H of G. Then it is shown that B satisfies the fundamental theorem if and only if B is one of the following three types: (1) B is an indecomposable commutative Galois algebra, (2) B = Re ⊕ R(1 ? e) where e and 1 ? e are minimal central idempotents in B, and (3) B is an indecomposable Galois algebra such that for each separable subalgebra A, V B (A) = ?∑ g∈G(A) J g , and the centers of A and B G(A) are the same where V B (A) is the commutator subring of A in B, J g = {b ∈ B | bx = g(x)b for each x ∈ B} for a g ∈ G, and G(A) = {g ∈ G | g(a) = a for all a ∈ A}. 相似文献
6.
7.
《代数通讯》2013,41(3):1453-1474
Abstract Let 𝕂 be a field of characteristic zero, and R be a G-graded 𝕂-algebra. We consider the algebra R ? E, then deduce its G × ?2-graded polynomial identities starting from the G-graded polynomial identities of R. As a consequence, we describe a basis for the ? n × ?2-graded identities of the algebras M n (E). Moreover we give the graded cocharacter sequence of M 2(E), and show that M 2(E) is PI-equivalent to M 1,1(E) ? E. This fact is a particular case of a more general result obtained by Kemer. 相似文献
8.
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
9.
10.
Let E/F be a Galois extension of number fields with the quaternion Galois group Q 8. In this paper, we prove some relations connecting orders of the odd part of the kernel of the transfer map of the tame kernel of E with the same orders of some of its subfields. Let E/? be a Galois extension of number fields with the Galois group Q 8 and p an odd prime such that p ≡ 3 (mod 4). We prove that if there is at most one quadratic subfield such that the p-Sylow subgroup of the tame kernel is nontrivial, then p r -rank(K 2(E/K)) is even, i.e., 2|p r -rank(K 2(𝒪 E )) ? p r -rank(K 2(𝒪 K )), where K is the quartic subfield of E. 相似文献
11.
Boris Širola 《代数通讯》2013,41(9):3267-3279
Suppose G 1 ? G are complex linear simple Lie groups. Let 1 ? be the corresponding pair of Lie algebras. For the Killing-orthogonal of 1 in we have a vector space direct sum = 1⊕ , which generalizes the classical Cartan decomposition on the Lie algebras level. In this article we study the corresponding problem of a ‘generalized global Cartan decomposition’ on the Lie groups level for the pair of groups ( G , G 1) = (SL (4,?),Sp (2,?)); here = (4,?), 1 = (2,?), and = {X ? | X ? = X}, where X? X ? is the symplectic involution. We prove that G = G 1exp ∪ i G 1exp . The key point of the proof is to study in detail the set exp ; and for that purpose we introduce the J-twisted Pfaffian of size 2n defined on the set of all 2n × 2n matrices X satisfying X ? = X, which is here a natural counterpart of the standard Pfaffian. 相似文献
12.
A weak Cayley table isomorphism is a bijection φ: G → H of groups such that φ(xy) ~ φ(x)φ(y) for all x, y ∈ G. Here ~denotes conjugacy. When G = H the set of all weak Cayley table isomorphisms φ: G → G forms a group 𝒲(G) that contains the automorphism group Aut(G) and the inverse map I: G → G, x → x ?1. Let 𝒲0(G) = ?Aut(G), I? ≤ 𝒲(G) and say that G has trivial weak Cayley table group if 𝒲(G) = 𝒲0(G). We show that all finite irreducible Coxeter groups (except possibly E 8) have trivial weak Cayley table group, as well as most alternating groups. We also consider some sporadic simple groups. 相似文献
13.
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
14.
15.
Bijan Taeri 《代数通讯》2013,41(3):894-922
Let n be an integer greater than 1. A group G is said to be “ n-rewritable” whenever for every n elements x 1,…,x n of G, there exist distinct permutations τ, σ on the set {1,2,…, n} such that x τ(1) ··· x τ(n) = x σ (1) ··· x σ (n). In this article, we complete the classification of 3-rewritable finite nilpotent groups and prove that a finite nilpotent group G is 3-rewritable if and only if G has an abelian subgroup of index 2 or the derived subgroup has order < 6. 相似文献
16.
Guangquan Guo 《代数通讯》2013,41(6):2269-2280
In this article, the notions of a Frobenius pair of functors and Frobenius corings are generalized to an l-QF pair of functors and l-QF corings. We prove that an extension ι:B → A is left quasi-Frobenius if and only if (F 1,G 1) is an l-QF pair of functors, where F 1: A ? → B ? is the restriction of scalars functors, and G 1 = A? B ? : B ? → A ? is the induction functor. For an A-coring , we prove that is an l-QF coring if and only if A → ? is an l-QF extension and A is a finitely generated projective modules if and only if (G 2,F 2) is an l-QF pair of functors, where G 2 = ? A ? : A ? → ? is the induction functor, F 2: ? → A ? is the forgetful functor, the result of Brzezinski is generalized. 相似文献
17.
In this article we prove that a set of points B of PG(n, 2) is a minimal blocking set if and only if ?B? = PG(d, 2) with d odd and B is a set of d + 2 points of PG(d, 2) no d + 1 of them in the same hyperplane. As a corollary to the latter result we show that if G is a finite 2-group and n is a positive integer, then G admits a ? n+1-cover if and only if n is even and G? (C 2) n , where by a ? m -cover for a group H we mean a set 𝒞 of size m of maximal subgroups of H whose set-theoretic union is the whole H and no proper subset of 𝒞 has the latter property and the intersection of the maximal subgroups is core-free. Also for all n < 10 we find all pairs (m,p) (m > 0 an integer and p a prime number) for which there is a blocking set B of size n in PG(m,p) such that ?B? = PG(m,p). 相似文献
18.
Pablo Ramacher 《偏微分方程通讯》2013,38(4):515-546
ABSTRACT Let G be a connected, linear algebraic group defined over ?, acting regularly on a finite dimensional vector space V over ? with ?-structure V ?. Assume that V possesses a Zariski-dense orbit, so that (G, ?, V) becomes a prehomogeneous vector space over ?. We consider the left regular representation π of the group of ?-rational points G ? on the Banach space C0(V ?) of continuous functions on V ? vanishing at infinity, and study the convolution operators π(f), where f is a rapidly decreasing function on the identity component of G ?. Denote the complement of the dense orbit by S, and put S ? = S ∩ V ?. It turns out that, on V ? ? S ?, π(f) is a smooth operator. If S ? = {0}, the restriction of the Schwartz kernel of π(f) to the diagonal defines a homogeneous distribution on V ? ? {0}. Its nonunique extension to V ? can then be regarded as a trace of π(f). If G is reductive, and S and S ? are irreducible hypersurfaces, π(f) corresponds, on each connected component of V ? ? S ?, to a totally characteristic pseudodifferential operator. In this case, the restriction of the Schwartz kernel of π(f) to the diagonal defines a distribution on V ? ? S ? given by some power |p(m)| s of a relative invariant p(m) of (G, ?, V) and, as a consequence of the Fundamental Theorem of Prehomogeneous Vector Spaces, its extension to V ?, and the complex s-plane, satisfies functional equations similar to those for local zeta functions. A trace of π(f) can then be defined by subtracting the singular contributions of the poles of the meromorphic extension. 相似文献
19.
Johan Öinert 《代数通讯》2013,41(2):831-841
Necessary and sufficient conditions for simplicity of a general skew group ring A ?σ G are not known. In this article, we show that a skew group ring A ?σ G, of an abelian group G, is simple if and only if its centre is a field and A is G-simple. As an application, we show that a transformation group (X, G), where X is a compact Hausdorff space acted upon by an abelian group G, is minimal and faithful if and only if its associated skew group algebra C(X) ?σ G is simple. 相似文献
20.
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