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We prove that if G is a finite simple group which is the unit group of a ring, then G is isomorphic to: (a) a cyclic group of order 2; or (b) a cyclic group of prime order 2k−1 for some k; or (c) a projective special linear group PSLn(F2) for some n≥3. Moreover, these groups do all occur as unit groups. We deduce this classification from a more general result, which holds for groups G with no non-trivial normal 2-subgroup. 相似文献
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For a non-degenerate convex subset Y of the n -dimensional Euclidean space Rn, let F(Y) be the family of all fuzzy sets of Rn which are upper semicontinuous, fuzzy convex and normal with compact supports contained in Y . We show that the space F(Y) with the topology of sendograph metric is homeomorphic to the separable Hilbert space ?2 if Y is compact; and the space F(Rn) is also homeomorphic to ?2. 相似文献
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We prove that if for a continuous map f on a compact metric space X, the chain recurrent set, R(f) has more than one chain component, then f does not satisfy the asymptotic average shadowing property. We also show that if a continuous map f on a compact metric space X has the asymptotic average shadowing property and if A is an attractor for f, then A is the single attractor for f and we have A=R(f). We also study diffeomorphisms with asymptotic average shadowing property and prove that if M is a compact manifold which is not finite with dimM=2, then the C1 interior of the set of all C1 diffeomorphisms with the asymptotic average shadowing property is characterized by the set of Ω-stable diffeomorphisms. 相似文献
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Let F be either the real number field R or the complex number field C and RPn the real projective space of dimension n. Theorems A and C in Hemmi and Kobayashi (2008) [2] give necessary and sufficient conditions for a given F-vector bundle over RPn to be stably extendible to RPm for every m?n. In this paper, we simplify the theorems and apply them to the tangent bundle of RPn, its complexification, the normal bundle associated to an immersion of RPn in Rn+r(r>0), and its complexification. Our result for the normal bundle is a generalization of Theorem A in Kobayashi et al. (2000) [8] and that for its complexification is a generalization of Theorem 1 in Kobayashi and Yoshida (2003) [5]. 相似文献
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A group-word w is called concise if whenever the set of w-values in a group G is finite it always follows that the verbal subgroup w(G) is finite. More generally, a word w is said to be concise in a class of groups X if whenever the set of w-values is finite for a group G∈X, it always follows that w(G) is finite. P. Hall asked whether every word is concise. Due to Ivanov the answer to this problem is known to be negative. Dan Segal asked whether every word is concise in the class of residually finite groups. In this direction we prove that if w is a multilinear commutator and q is a prime-power, then the word wq is indeed concise in the class of residually finite groups. Further, we show that in the case where w=γk the word wq is boundedly concise in the class of residually finite groups. It remains unknown whether the word wq is actually concise in the class of all groups. 相似文献
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Consider a face-to-face parallelohedral tiling of Rd and a (d−k)-dimensional face F of the tiling. We prove that the valence of F (i.e. the number of tiles containing F as a face) is not greater than 2k. If the tiling is affinely equivalent to a Voronoi tiling for some lattice (the so called Voronoi case), this gives a well-known upper bound for the number of vertices of a Delaunay k-cell. Yet we emphasize that such an affine equivalence is not assumed in the proof. 相似文献
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Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are Lipschitz ?-strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
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Let k be any field, G be a finite group acting on the rational function field k(xg:g∈G) by h⋅xg=xhg for any h,g∈G. Define k(G)=k(xg:g∈G)G. Noether’s problem asks whether k(G) is rational (= purely transcendental) over k. A weaker notion, retract rationality introduced by Saltman, is also very useful for the study of Noether’s problem. We prove that, if G is a Frobenius group with abelian Frobenius kernel, then k(G) is retract k-rational for any field k satisfying some mild conditions. As an application, we show that, for any algebraic number field k, for any Frobenius group G with Frobenius complement isomorphic to SL2(F5), there is a Galois extension field K over k whose Galois group is isomorphic to G, i.e. the inverse Galois problem is valid for the pair (G,k). The same result is true for any non-solvable Frobenius group if k(ζ8) is a cyclic extension of k. 相似文献
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In this paper, we first investigate coefficient estimates for bounded polyharmonic mappings in the unit disk D. Then, we obtain two versions of Landau’s theorem for polyharmonic mappings F, and for the mappings of the type L(F), where L is the differential operator of Abdulhadi, Abu Muhanna and Khuri. Examples and numerical estimates are given. 相似文献
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We give examples of closed orientable graph 3-manifolds having a fundamental group which is not a subgroup of GL(4,F) for any field F. This answers a question in the Kirby problem list from 1977 which is credited to the late William Thurston. 相似文献
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Let F be an algebraically closed field. Let V be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form B over F. Suppose the characteristic of F is sufficiently large , i.e. either zero or greater than the dimension of V. Let I(V,B) denote the group of isometries. Using the Jacobson–Morozov lemma we give a new and simple proof of the fact that two elements in I(V,B) are conjugate if and only if they have the same elementary divisors. 相似文献
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