共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove that the octonionic polynomials V ■k l 1 ··· l k are independent of the associative orders ■k . This improves the octonionic Taylor type theorem. 相似文献
2.
With the newly developed octonion analytic function theory, we confirm the octonionic analogue of the Calderón's conjecture. As application, we obtain the Plemelj formula in octonionic space. 相似文献
3.
《复变函数与椭圆型方程》2012,57(13):1031-1040
It is shown that there is only one possible way to define the O-analytic functions. A simple way to construct the O-analytic functions is also given. 相似文献
4.
N. I. Sandu 《Mathematical Notes》1999,66(2):217-222
With the help of the relationship between commutative Moufang loops and alternative commutative algebras, we prove, rather
easily, the following weakened version of the Bruck-Slaby theorem: a finitely generated commutative Moufang loop is centrally
nilpotent.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 275–281, August, 1999. 相似文献
5.
If the order of any product of two different translations of a finite Steiner quasigroup of size n>3 is odd, then the group G generated by the translations of the corresponding Steiner loop of order n+1 contains the alternating group of degree n+1. 相似文献
6.
Summary An RA loop is a (necessarily Moufang) loop whose loop rings in any characteristic are alternative, but not associative. There
are seven classes of finite indecomposable RA loops. In this paper, we find the indecomposable subloops and the indecomposable
nonabelian groups which can appear inside the loops in each class. 相似文献
7.
We shall show how the nilpotency class of a finite loop Q is determined by the properties of a nilpotent inner mapping group. We also show that a classical result by Baer on the structure
of abelian finite capable groups holds for Moufang loops of odd order. 相似文献
8.
We describe Steiner loops of nilpotency class 2 and establish the classification of finite 3-generated nilpotent Steiner loops of nilpotency class 2. 相似文献
9.
S. V. Konyagin 《Mathematical Notes》2008,84(3-4):435-438
10.
Umberto Marconi 《Rendiconti del Circolo Matematico di Palermo》2001,50(3):543-546
The purpose of this note is proving a result of Nogura and Shakhmatov [4, Theorem 4]. Furthermore, a characterization of connected
spaces with a selection is given.
Work supported by the research project “Metodi e problemi in Analisi Reale” of the Italian Ministero dell'Università e della
Ricerca Scientifica e Tecnologica. 相似文献
11.
Charles Thas 《Journal of Geometry》1996,57(1-2):197-202
The main result of this paper is a theorem about projectivities in then-dimensional complex projective spaceP
n (n 2). Puttingn = 2, we showed in [3] that the theorem of Desargues inP
n is a special case of this theorem. And not only the theorem of Desargues but also the converse of the theorem of Pascal, the theorem of Pappus-Pascal, the theorem of Miquel, the Newton line, the Brocard points and a lot of lesser known results in the projective, the affine and the Euchdean plane were obtained from this theorem as special cases without any further proof. Many extensions of classical theorems in the projective, affine and Euclidean plane to higher dimensions can be found in the literature and probably some of these are special cases of this theorem inP
n. We only give a few examples and leave it as an open problem which other special cases could be found. 相似文献
12.
New conditions for a planar homoclinic loop to have cyclicity two under multiple parameter perturbations have been obtained.
As an application it is proved that a homoclinic loop of a nongeneric cubic Hamiltonian has cyclicity two under arbitrary
quadratic perturbations.
Project supported by the National Natural Science Foundation of China (Grant Nos. 19531070 and 19771037). 相似文献
13.
Hugo Rodríguez-Ordez 《Expositiones Mathematicae》2007,25(4):355-361
This paper is a revision of a portion of the author's doctoral dissertation submitted to the University of Oregon. Using elementary concepts of K-theory, the Brouwer degree of the power map in the octonions is computed. Later, a proof of a weaker version of the fundamental theorem of algebra for polynomials with coefficients in the octonions is given. As a partial complement, a lower bound to the number of solutions of a homogeneous monomial equation over the octonions is obtained. 相似文献
14.
15.
It is well known that there is a planar sloop of cardinality n for each n≡2 or 4 (mod 6) (Math. Z. 111 (1969) 289–300). A semi-planar sloop is a simple sloop in which each triangle either generates the whole sloop or the 8-element sloop. In fact, Quackenbush (Canad. J. Math. 28 (1976) 1187–1198) has stated that there should be such semi-planar sloops. In this paper, we construct a semi-planar sloop of cardinality 2n for each n≡2 or 4 (mod 6). Consequently, we may say that there is a semi-planar sloop that is not planar of cardinality m for each m>16 and m≡4 or 8 (mod 12). Moreover, Quackenbush (Canad. J. Math. 28 (1976) 1187–1198) has proved that each finite simple planar sloop generates a variety, which covers the smallest non-trivial subvariety (the variety of all Boolean sloops) of the lattice of the subvarieties of all sloops. Similarly, it is easy to show that each finite semi-planar sloop generates another variety, which also covers the variety of all Boolean sloops. Furthermore, for any finite simple sloop
of cardinality n, the author (Beiträge Algebra Geom. 43 (2) (2002) 325–331) has constructed a subdirectly irreducible sloop
of cardinality 2n and containing
as the only proper normal subsloop. Accordingly, if
is a semi-planar sloop, then the variety
generated by
properly contains the subvariety
. 相似文献
16.
We introduce a web loop (P,
, +) which is precisely a loop (P,+) provided with the structure
of a web such that both structures are compatible in the sense that for eacha P the map a+PP;xa+x is an automorphism of (P,
). Exploiting the results of [6, 7, 9, Z] for the case of a web, we study web loops, webs with reflection structures and webs with point reflection structures.Dedicated to Professor Dr. Dr. h. c. Helmut Karzel on the occasion of his seventieth birthdayThis work was supported by CHONNAM NATIONNAL UNIVERSITY RESEARCH FUND, 1996 相似文献
17.
Ivan P. Shestakov 《Proceedings of the American Mathematical Society》2004,132(2):313-316
Let be the algebra of classical real octonions or the (split) algebra of octonions over the finite field 2$">. Then the quotient loop of the Moufang loop of all invertible elements of the algebra modulo its center is not embedded into a loop of invertible elements of any alternative algebra.
18.
Qingjun Kong 《Monatshefte für Mathematik》2014,175(1):133-138
Suppose that \(G\) is a finite group and \(H\) is a subgroup of \(G\) . \(H\) is said to be \(s\) -quasinormally embedded in \(G\) if for each prime \(p\) dividing the order of \(H\) , a Sylow \(p\) -subgroup of \(H\) is also a Sylow \(p\) -subgroup of some \(s\) -quasinormal subgroup of \(G\) . We fix in every non-cyclic Sylow subgroup \(P\) of \(G\) some subgroup \(D\) satisfying \(1<|D|<|P|\) and study the \(p\) -nilpotency of \(G\) under the assumption that every subgroup \(H\) of \(P\) with \(|H|=|D|\) is \(s\) -quasinormally embedded in \(G\) . Some recent results and the Frobenius \(^{\prime }\) theorem are generalized. 相似文献
19.
Quaternions are an important tool that provides a convenient and effective mathematical method for representing reflections and rotations in three-dimensional space. A unit timelike split quaternion represents a rotation in the Lorentzian space. In this paper, we give some geometric interpretations of split quaternions for lines and planes in the Minkowski 3-space with the help of mutual pseudo orthogonal planes. We classified mutual planes with respect to the casual character of the normals of the plane as follows; if the normal is timelike, then the mutual plane is isomorphic to the complex plane; if the normal is spacelike, then the plane is isomorphic to the hyperbolic number plane (Lorentzian plane); if the normal is lightlike, then the plane is isomorphic to the dual number plane (Galilean plane). 相似文献
20.
Let p be a prime number and let be the Vandermonde matrix with -entry equal to for , where ω is a primitive pth root of unity in the complex field. The classical Chebotarëv theorem says that all square submatrices of have nonzero determinant. In this paper, we establish the Chebotarëv theorem over finite fields by imposing certain conditions. 相似文献