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1.
For a group G, let M(G) denote the near-ring of functions on G. We characterize all maximal subnear-rings of M(G) and show that for many classes of groups, E(G), the near-ring generated by the semigroup, End(G) of G, is never maximal as a subnear-ring of M 0 (G). Received: 25 April 2008  相似文献   

2.
C. J. Maxson 《代数通讯》2017,45(1):384-391
For several classes of groups G, we characterize when the near-ring M0(G) of 0-preserving selfmaps on G contains a unique maximal ring. Definitive results are obtained for finite Abelian, finite nilpotent, and finite permutation groups. As an application, we determine those finite groups G such that all rings in M0(G) are commutative.  相似文献   

3.
Let M(G) denote the convolution algebra of finite regular complex-valued Borel measures on a locally compact abelian group G, and let M0(G) be the ideal consisting of those measures whose Fourier-Stieltjes transforms vanish at infinity. Then there is a natural inclusion of the maximal ideal space Δ0 of M0(G) in the maximal ideal space of M(G). The main result states that any subset of Δ0 which is a boundary for M0(G) is a boundary for M(G). An immediate corollary is that the ?ilov boundary of M0(G) is dense in the ?ilov boundary of M(G).  相似文献   

4.
Torsion-free Abelian groups G and H are called quasi-equal (GH) if λGHG for a certain natural number ≈. It is known (see [3]) that the quasi-equality of torsion-free Abelian groups can be represented as the equality in an appropriate factor category. Thus while dealing with certain group properties it is usual to prove that the property under consideration is preserved under the transition to a quasi-equal group. This trick is especially frequently used when the author investigates module properties of Abelian groups; here a group is considered as a left module over its endomorphism ring. On the other hand, a topical problem in the Abelian group theory is the problem of investigation of pureness in the category of Abelian groups (see [4]). We consider the pureness introduced by P. Cohn [2] for Abelian groups as modules over their endomorphism rings. Particularity of the investigation of the properties of pureness for the Abelian group G as the module E (G)G lies in the fact that this is a more general situation than the investigation of pureness for a unitary module over an arbitrary ring R with the identity element. Indeed, if R M is an arbitrary unitary left module and M + is its Abelian group, then each element from R can be identified with an appropriate endomorphism from the ring E(M +) under the canonical ring homomorphism RE(M +). Then it holds that if E(M+) N is a pure submodule in E(M+) M +, then R N is a pure submodule in R M. In the present paper the interrelations between pureness, servantness, and quasi-decompositions for Abelian torsion-free groups of finite rank will be investigated. __________ Translated from Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 2, pp. 225–238, 2004.  相似文献   

5.
Let 〈G, +〉 be a finite (not necessarily abelian) group. Then M0(G) := {f : GG| f (0) = 0} is a near-ring, i.e., a group which is also closed under composition of functions. In Theorem 4.1 we give lower and upper bounds for the fraction of the bijections which generate the near-ring M0(G). From these bounds we conclude the following: If G has few involutions and the order of G is large, then a high fraction of the bijections generate the near-ring M0(G). Also the converse holds: If a high fraction of the bijections generate M0(G), then G has few involutions (compared to the order of G). Received: 10 January 2005  相似文献   

6.
Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal sub-group of G. For principal fibre bundle (E,p, E,/G;G) tmd (E/H,p‘,E/G;G/H), the relation between auta(E) (resp. autce (E)) and autG/H(E/H) (resp. autGe/H(E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group JG(E) (resp. SG(E)) while the group J G/u(E/H) is known.  相似文献   

7.
A B-Injector in an arbitrary finite group G is defined as a maximal nilpo-tent subgroup of G, containing a subgroup A of G of maximal order satisfying class(A) ≥ 2. Among other results the B-Injectors of the sporadic groups J1,J2,J4, M24 are determined.  相似文献   

8.
Let G be a finite group, and let π e (G) be the spectrum of G, that is, the set of all element orders of G. In 1987, Shi Wujie put forward the following conjecture. If G is a finite group and M is a non-abelian simple group, then GM if and only if |G| = |M| and π e (G) = π e (M). In this short paper, we prove that if G is a finite group, then GM if and only if |G| = |M| and π e (G) = π e (M), where M = D n (2) and n is even.  相似文献   

9.
A group G is said to satisfy the maximal permutizer condition if the permutizer of any maximal subgroup M of G in G, PG(M), is G. In this paper, we characterize the supersolubility of finite groups by using the maximal permutizer condition. We also get some results for when both G/N and N are supersoluble, which implies that G is supersoluble. Our results unify or generalize some known results.  相似文献   

10.
Let G be an infinite pro-p-group of finite coclass and let M(G) be its Schur multiplicator. For p > 2, we determine the isomorphism type of Hom(M(G), ℤp), where ℤp denotes the p-adic integers, and show that M(G) is infinite. For p = 2, we investigate the Schur multiplicators of the infinite pro-2-groups of small coclass and show that M(G) can be infinite, finite or even trivial.  相似文献   

11.
All normal subloops of a loopG form a modular latticeL n (G). It is shown that a finite loopG has a complemented normal subloop lattice if and only ifG is a direct product of simple subloops. In particular,L n (G) is a Boolean algebra if and only if no two isomorphic factors occurring in a decomposition ofG are abelian groups. The normal subloop lattice of a finite loop is a projective geometry if and only ifG is an elementary abelianp-group for some primep.  相似文献   

12.
For a class of groupsF, closed under formation of subgroups and products, we call a subgroupA of a groupG F-regular provided there are two homomorphismsf, g: G » F, withF F, so thatA = {x G |f(x) =g(x)}.A is calledF-normal providedA is normal inG andG/A F. For an arbitrary subgroupA ofG, theF-regular (respectively,F-normal) closure ofA inG is the intersection of allF-regular (respectively,F-normal) subgroups ofG containingA. This process gives rise to two well behaved idempotent closure operators.A groupG is calledF-regular (respectively,F-normal) compact provided for every groupH, andF-regular (respectively,F-normal) subgroupA ofG × H, 2(A) is anF-regular (respectively,F-normal) subgroup ofH. This generalizes the well known Kuratowski-Mrówka theorem for topological compactness.In this paper, theF-regular compact andF-normal compact groups are characterized for the classesF consisting of: all torsion-free groups, allR-groups, and all torsion-free abelian groups. In doing so, new classes of groups having nice properties are introduced about which little is known.  相似文献   

13.
We study Hilbert functions of maximal CM modules over CM local rings. When A is a hypersurface ring with dimension d>0, we show that the Hilbert function of M with respect to is non-decreasing. If A=Q/(f) for some regular local ring Q, we determine a lower bound for e0(M) and e1(M) and analyze the case when equality holds. When A is Gorenstein a relation between the second Hilbert coefficient of M, A and SA(M)= (SyzA1(M*))* is found when G(M) is CM and depthG(A)≥d−1. We give bounds for the first Hilbert coefficients of the canonical module of a CM local ring and analyze when equality holds. We also give good bounds on Hilbert coefficients of M when M is maximal CM and G(M) is CM.  相似文献   

14.
This paper concerns the problem of irreducible decompositions of unitary representations of topological groups G, including the group Diff0(M) of diffeomorphisms with compact support on smooth manifolds M. It is well known that the problem is affirmative, when G is a locally compact, separable group (cf. [3, 4]). We extend this result to infinite-dimensional groups with appropriate quasi-invariant measures, and, in particular, we show that every continuous unitary representation of Diff0(M) has an irreducible decomposition under a fairly mild condition. This research was partially supported by a Grant-in-Aid for Scientific Research (No.14540167), Japan Socieity of the Promotion of Science.  相似文献   

15.
We define a discrete groupW(E) associated to a faithful normal conditional expectationE : M N forN M von Neuman algebras. This group shows the relation between the unitary groupU N and the normalizerN E ofE, which can be also considered as the isotropy of the action of the unitary groupU M ofM onE. It is shown thatW(E) is finite if dimZ(N)< and bounded by the index in the factor case. Also sharp bounds of the order ofW(E) are founded.W(E) appears as the fibre of a covering space defined on the orbit ofE by the natural action of the unitary group ofM. W(E) is computed in some basic examples.  相似文献   

16.
For a finite group scheme G over a field k of characteristic p>0, we associate new invariants to a finite dimensional kG-module M. Namely, for each generic point of the projectivized cohomological variety we exhibit a “generic Jordan type” of M. In the very special case in which G=E is an elementary abelian p-group, our construction specializes to the non-trivial observation that the Jordan type obtained by restricting M via a generic cyclic shifted subgroup does not depend upon a choice of generators for E. Furthermore, we construct the non-maximal support variety Γ(G) M , a closed subset of which is proper even when the dimension of M is not divisible by p.  相似文献   

17.
By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. For a given finite group G, let c(G) denote the minimal degree of a faithful representation of G by complex quasi-permutation matrices and let r(G) denote the minimal degree of a faithful rational valued character of G. Also let G denote one of the symbols Al, Bl, Cl, Dl, E6, E7, E8, G2, F4, 2B2, 2E4, 2G2, and 3D4. Let G(q) denote simple group of type G over GF(q). Let c(q) = c(G(q)) and r(q) = r(G(q)). Then we will show that lim Limq = 1.  相似文献   

18.
In [5], Navarro defines the set , where Q is a p-subgroup of a p-solvable group G, and shows that if δ is the trivial character of Q, then Irr(G|Q, δ) provides a set of canonical lifts of IBrp(G), the irreducible Brauer characters with vertex Q. Previously, in [2], Isaacs defined a canonical set of lifts Bπ(G) of Iπ(G). Both of these results extend the Fong-Swan Theorem to π-separable groups, and both construct canonical sets of lifts of the generalized Brauer characters. It is known that in the case that 2∈π, or if |G| is odd, we have Bπ(G) = Irr(G|Q, 1Q). In this note we give a counterexample to show that this is not the case when . It is known that if and χ∈Bπ(G), then the constituents of χN are in Bπ (N). However, we use the same counterexample to show that if , and χ∈Irr(G|Q, 1Q) is such that θ ∈Irr(N) and [θ, χ N] ≠ 0, then it is not necessarily the case that θ ∈Irr(N) inherits this property. Received: 17 October 2005  相似文献   

19.
We define a notion of complexity for modules over group rings of infinite groups. This generalizes the notion of complexity for modules over group algebras of finite groups. We show that if M is a module over the group ring kG, where k is any ring and G is any group, and M has f-complexity (where f is some complexity function) over some set of finite index subgroups of G, then M has f-complexity over G (up to a direct summand). This generalizes the Alperin-Evens Theorem, which states that if the group G is finite then the complexity of M over G is the maximal complexity of M over an elementary abelian subgroup of G. We also show how we can use this generalization in order to construct projective resolutions for the integral special linear groups, SL(n, ℤ), where n ≥ 2.  相似文献   

20.
For a compact subset K in the complex plane, let A(K) denote the algebra of all functions continuous on K and analytic on K° and let R(K) denote the uniform closure of the rational functions with poles off K. Let G is a bounded open subset whose complement in the plane has a finite number of components. Suppose that and every function in H(G) is the pointwise limit of a bounded sequence of functions in . The purpose of this paper is to characterize all subnormal operators similar to Mz, the operator of multiplication by the independent variable z on the Hardy space H2(G). We also characterize all bounded linear operators that are unitarily equivalent to Mz in the case when each of the components of G is simply connected. In particular, our similarity result extends a well-known result of W. Clary on the unit disk to multiply connected domains.  相似文献   

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