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1.
Let V be a nonsingular vector space over a field K of characteristic 2 with |K|>3. Suppose K is perfect and π is an element in the special orthogonal group SO(V)=Ω(V) with dimB(π)=2d. The length of π with respect to the symmetry commutators is d if B(π) is not totally isotropic; otherwise it is d+1. 相似文献
2.
Let R denote a commutative local ring with maximal ideal m and residue field K = R/m. Let V be a symplectic space over R. In this paper we determine the group automorphisms of the symplectic group Spn(V) when n 6, the characteristic of k is not 2, and k is not the finite field of three elements. 相似文献
3.
Group Connectivity of 3-Edge-Connected Chordal Graphs 总被引:3,自引:0,他引:3
Hong-Jian Lai 《Graphs and Combinatorics》2000,16(2):165-176
Let A be a finite abelian group and G be a digraph. The boundary of a function f: E(G)ZA is a function f: V(G)ZA given by f(v)=~e leaving vf(e)m~e entering vf(e). The graph G is A-connected if for every b: V(G)ZA with ~v] V(G) b(v)=0, there is a function f: E(G)ZA{0} such that f=b. In [J. Combinatorial Theory, Ser. B 56 (1992) 165-182], Jaeger et al showed that every 3-edge-connected graph is A-connected, for every abelian group A with |A|̈́. It is conjectured that every 3-edge-connected graph is A-connected, for every abelian group A with |A|̓ and that every 5-edge-connected graph is A-connected, for every abelian group A with |A|́.¶ In this note, we investigate the group connectivity of 3-edge-connected chordal graphs and characterize 3-edge-connected chordal graphs that are A-connected for every finite abelian group A with |A|́. 相似文献
4.
Hiroyuki Ishibashi 《Journal of Pure and Applied Algebra》1981,22(2):121-129
This paper is devoted to determine the minimal length of expressions of an isometry in a symplectic group Spn(V) by a product of transvections under the assumption that V is an n-ary nonsingular alternating space over a quasi semilocal semihereditary ring with 2 as a unit. 相似文献
5.
A.A. Baranov 《Archiv der Mathematik》1999,72(2):101-106
An algebra is called finitary if it consists of finite-rank transformations of a vector space. We classify finitary simple Lie algebras over an algebraically closed field of zero characteristic. It is shown that any such algebra is isomorphic to one of the following¶ (1) a special transvection algebra
\frak t(V,P)\frak t(V,\mit\Pi );¶ (2) a finitary orthogonal algebra
\frak fso (V,q)\frak {fso} (V,q); ¶ (3) a finitary symplectic algebra
\frak fsp (V,s)\frak {fsp} (V,s).¶Here V is an infinite dimensional K-space; q (respectively, s) is a symmetric (respectively, skew-symmetric) nondegenerate bilinear form on V; and P\Pi is a subspace of the dual V* whose annihilator in V is trivial: 0={v ? V | Pv=0}0=\{{v}\in V\mid \Pi {v}=0\}. 相似文献
6.
Let D be a simple digraph without loops or digons. For any v ? V(D) v\in V(D) , the first out-neighborhood N+(v) is the set of all vertices with out-distance 1 from v and the second neighborhood N++(v) of v is the set of all vertices with out-distance 2 from v. We show that every simple digraph without loops or digons contains a vertex v such that |N++(v)| 3 g|N+(v)| |N^{++}(v)|\geq\gamma|N^+(v)| , where % = 0.657298... is the unique real root of the equation 2x3 + x2 -1 = 0. 相似文献
7.
Let V be an n-dimensional affine space over the field with pd elements, p ≠ 2. Then for every ε > 0 there is an n(ε) such that if n = dim(V) ? n(ε) then any subset of V with more than ε|V| elements must contain 3 collinear points (i.e., 3 points lying in a one-dimensional affine subspace). 相似文献
8.
Let Un(V) and Spn(V) denote the unitary group and the symplectic group of the n dimensional vector space V over a finite field of characteristic not 2, respectively. Assume that the hyperbolic rank of Un(V) is at least one. Then Un(V) is generated by 4 elements and Spn(V) by 3 elements. Further, U2m+1(V) is generated by 3 elements and Sp4m(V) by 2 elements. 相似文献
9.
J. Brzdek 《Aequationes Mathematicae》2000,59(3):248-254
Summary. Let \Bbb K {\Bbb K} be either the field of reals or the field of complex numbers, X be an F-space (i.e. a Fréchet space) over \Bbb K {\Bbb K} n be a positive integer, and f : X ? \Bbb K f : X \to {\Bbb K} be a solution of the functional equation¶¶f(x + f(x)n y) = f(x) f(y) f(x + f(x)^n y) = f(x) f(y) .¶We prove that, if there is a real positive a such that the set { x ? X : |f(x)| ? (0, a)} \{ x \in X : |f(x)| \in (0, a)\} contains a subset of second category and with the Baire property, then f is continuous or { x ? X : |f(x)| ? (0, a)} \{ x \in X : |f(x)| \in (0, a)\} for every x ? X x \in X . As a consequence of this we obtain the following fact: Every Baire measurable solution f : X ? \Bbb K f : X \to {\Bbb K} of the equation is continuous or equal zero almost everywhere (i.e., there is a first category set A ì X A \subset X with f(X \A) = { 0 }) f(X \backslash A) = \{ 0 \}) . 相似文献
10.
Edward A Connors 《Journal of Number Theory》1973,5(6):477-501
Let V be a nondefective quadratic space over a field F of characteristic 2. Assume that V has dimension at least ten and that F has more than two elements. Let Δ be one of the groups O(V), O+(V), O′(V), or (the full orthogonal group, the rotation group, the spinorial kernel, or the commutator subgroup of O(V), respectively). Then Λ is an automorphism of Λ if and only if Λ(σ) = gσg?1 for all σ in Δ where g is a semilinear automorphism of V that preserves the quadratic structure of V in the sense that Q(gx) = αQ(x)u for all x in V where Q is the quadratic form, α is some nonzero element of F, and u is the field automorphism of F associated to g. 相似文献
11.
Let V be a vector space over a division ring K. Let P be a spanning set of points in Σ:=PG(V). Denote by K(P) the family of sub-division rings F of K having the property that there exists a basis BF of V such that all points of P are represented as F-linear combinations of BF. We prove that when K is commutative, then K(P) admits a least element. When K is not commutative, then, in general, K(P) does not admit a minimal element. However we prove that under certain very mild conditions on P, any two minimal elements of K(P) are conjugate in K, and if K is a quaternion division algebra then K(P) admits a minimal element. 相似文献
12.
Let K be a field of even characteristic,
V a finite-dimensional vector
space over K, and SO(V)
the special orthogonal group. Then SO(V) is
trireflectional, provided dim V > 2 and
SO(V) O+
(4, 2).
Received: 4 February 2003 相似文献
13.
Clément de Seguins Pazzis 《Linear algebra and its applications》2011,435(11):2708-2721
Let (K) be a field. Given an arbitrary linear subspace V of Mn(K) of codimension less than n-1, a classical result states that V generates the (K)-algebra Mn(K). Here, we strengthen this statement in three ways: we show that Mn(K) is spanned by the products of the form AB with (A,B)∈V2; we prove that every matrix in Mn(K) can be decomposed into a product of matrices of V; finally, when V is a linear perplane of Mn(K) and n>2, we show that every matrix in Mn(K) is a product of two elements of V. 相似文献
14.
R. D. Blyth 《Archiv der Mathematik》2002,78(5):337-344
Let n be an integer greater than 1, and let G be a group. A subset {x1, x2, ..., xn} of n elements of G is said to be rewritable if there are distinct permutations p \pi and s \sigma of {1, 2, ..., n} such that¶¶xp(1)xp(2) ?xp(n) = xs(1)xs(2) ?xs(n). x_{\pi(1)}x_{\pi(2)} \ldots x_{\pi(n)} = x_{\sigma(1)}x_{\sigma(2)} \ldots x_{\sigma(n)}. ¶¶A group is said to have the rewriting property Qn if every subset of n elements of the group is rewritable. In this paper we prove that a finite group of odd order has the property Q3 if and only if its derived subgroup has order not exceeding 5. 相似文献
15.
Steven H. Weintraub 《Journal of Geometry》2007,86(1-2):165-180
Let V be a vector space of dimension 2n, n even, over a field F, equipped with a nonsingular symplectic form. We define a new algebraic/combinatorial structure, a spread of nonsingular
pairs, or nsp-spread, on V and show that nsp-spreads exist in considerable generality. We further examine in detail some particular cases. 相似文献
16.
Let V be an n-dimensional Euclidean vector space, and let V(m) be the corresponding m-th completely symmetric space over V equipped with the induced inner product. The purpose of this paper is to prove the following conjecture of H.A. Robinson: if T is a linear operator on V(m) and (Tz, z) = 0 for every decomposable element z of V(m), then T is skew-symmetric. 相似文献
17.
Let G be a graph and n ≥ 2 an integer. We prove that the following are equivalent: (i) there is a partition (V1,…,Vm) of V (G) such that each Vi induces one of stars K1,1,…,K1,n, and (ii) for every subset S of V(G), G\ S has at most n|S| components with the property that each of their blocks is an odd order complete graph. © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 185–190, 1997 相似文献
18.
S. Tazhetdinov 《Mathematical Notes》2006,80(5-6):726-728
19.
The influence of S-quasinormality of some subgroups of prime power order on the structure of finite groups 总被引:1,自引:0,他引:1
M. Ramadan 《Archiv der Mathematik》2001,77(2):143-148
Let G be a finite group. Two subgroups H and K of G are said to permute if áH,K? = HK = KH\langle H,K\rangle = HK = KH. A subgroup H of G is S-quasinormal in G if it permutes with every Sylow subgroup of G. In this paper we investigate the influence of S-quasinormality of some subgroups of prime power order of a finite group on its supersolvability. 相似文献
20.
Egbert Harzheim 《Archiv der Mathematik》1999,73(2):114-118
Let n, a, d be natural numbers and A a set of integers of the closed interval [0, n] with | A | = a. Then we establish sharp lower and upper bounds for the number of pairs (x,y) ? A×A(x,y)\in A\times A for which y - x = d. Roughly spoken, we investigate how often a distance d can occur in A. 相似文献